Practical Circuitry for Measurement and Control Problems

Application Note 61
August 1994
Practical Circuitry for Measurement and Control Problems
Circuits Designed for a Cruel and Unyielding World
Jim Williams
INTRODUCTION
currents associated with the continuous operation of fixed
frequency designs. Gated oscillator regulators simply
self-clock at whatever frequency is required to maintain
the output voltage. Typically, loop oscillation frequency
ranges from a few hertz into the kilohertz region, depending upon the load.
This collection of circuits was worked out between June
1991 and July of 1994. Most were designed at customer
request or are derivatives of such efforts. All represent
substantial effort and, as such, are disseminated here
for wider study and (hopefully) use.1 The examples are
roughly arranged in categories including power conversion, transducer signal conditioning, amplifiers and signal
generators. As always, reader comment and questions
concerning variants of the circuits shown may be addressed
directly to the author.
In most cases this asynchronous, variable frequency operation does not create problems. Some systems, however, are
sensitive to this characteristic. Figure 1 slightly modifies
a gated oscillator type switching regulator by synchronizing its loop oscillation frequency to the systems clock. In
this fashion the oscillation frequency and its attendant
switching noise, albeit variable, become coherent with
system operation.
Clock Synchronized Switching Regulator
Gated oscillator type switching regulators permit high
efficiency over extended ranges of output current. These
regulators achieve this desirable characteristic by using
a gated oscillator architecture instead of a clocked pulse
width modulator. This eliminates the “housekeeping”
Note 1: “Study” is certainly a noble pursuit but we never fail to
emphasize use.
L, LT, LTC, LTM, Linear Technology and the Linear logo are registered trademarks of Linear
Technology Corporation. All other trademarks are the property of their respective owners.
VIN
2V TO 3.2V
(2 CELLS)
47Ω
100k
VIN
LT1107
–
AOUT
Q1
Q1
CLR2 PRE2
VCC
CLK1
D1
221k*
FB
+
100μF
82.5k*
COMP
Q2
GND CLK2
5VOUT
SW1
+
74HC74
FLIP-FLOP
CLR1
1N5817
AUXILIARY
AMP
VREF
1.2V
D2
ILIM
VREF
+
PRE1
L1
22μH
SET
OSCILLATOR
–
100k*
SW2
GND
47k
AN61 F01
100kHz CLOCK
POWERED FROM
5V OUTPUT
L1 = COILTRONICS CTX-20-2
*= 1% METAL FILM RESISTOR
Figure 1. A Synchronizing Flip-Flop Forces Switching Regulator Noise to Be Coherent with the Clock
an61fa
AN61-1
Application Note 61
Circuit operation is best understood by temporarily ignoring the flip-flop and assuming the LT®1107 regulator’s
AOUT and FB pins are connected. When the output voltage
decays the set pin drops below VREF, causing AOUT to
fall. This causes the internal comparator to switch high,
biasing the oscillator and output transistor into conduction. L1 receives pulsed drive, and its flyback events are
deposited into the 100μF capacitor via the diode, restoring
output voltage. This overdrives the set pin, causing the IC
to switch off until another cycle is required. The frequency
of this oscillatory cycle is load dependent and variable. If,
as shown, a flip-flop is interposed in the AOUT-FB pin path,
synchronization to a system clock results. When the output
decays far enough (trace A, Figure 2) the AOUT pin (trace B)
goes low. At the next clock pulse (trace C) the flip-flop Q2
output (trace D) sets low, biasing the comparator-oscillator.
This turns on the power switch (VSW pin is trace E), which
pulses L1. L1 responds in flyback fashion, depositing its
energy into the output capacitor to maintain output voltage. This operation is similar to the previously described
case, except that the sequence is forced to synchronize
with the system clock by the flip-flops action. Although the
resulting loops oscillation frequency is variable it, and all
attendant switching noise, is synchronous and coherent
with the system clock.
buffer. The CLR1-CLK1 line monitors output voltage via the
resistor string. When power is applied Q1 sets CLR2 low.
This permits the LT1107 to switch, raising output voltage.
When the output goes high enough Q1 sets CLR2 high
and normal loop operation commences.
A start-up sequence is required because this circuit’s
clock is powered from its output. The start-up circuitry
was developed by Sean Gold and Steve Pietkiewicz of
LTC. The flip-flop’s remaining section is connected as a
+
The circuit shown is a step-up type, although any switching regulator configuration can utilize this synchronous
technique.
High Power 1.5V to 5V Converter
Some 1.5V powered systems (survival 2-way radios,
remote, transducer-fed data acquisition systems, etc.)
require much more power than stand-alone IC regulators
can provide. Figure 3’s design supplies a 5V output with
200mA capacity.
The circuit is essentially a flyback regulator. The LT1170
switching regulator’s low saturation losses and ease of
use permit high power operation and design simplicity.
Unfortunately this device has a 3V minimum supply requirement. Bootstrapping its supply pin from the 5V output is
possible, but requires some form of start-up mechanism.
1.5VIN
47μF
L1
25μH
1N5823
+
VSW
VIN
GND
VC
B = 5V/DIV
470μF
FB
LT1170
A = 50mV/DIV
AC-COUPLED
3.74k*
5VOUT
200mA MAX
1k
+
6.8μF
C = 5V/DIV
1k*
SW1
VIN
D = 5V/DIV
SENSE
LT1073
ILIM
240Ω*
SW2
E = 5V/DIV
GND
AN61 F03
20μs/DIV
AN61 F02
Figure 2. Waveforms for the Clock Synchronized
Switching Regulator. Regulator Only Switches (Trace E)
on Clock Transitions (Trace C), Resulting in Clock
Coherent Output Noise (Trace A)
L1 = PULSE ENGINEERING #PE-92100
* = 1% METAL FILM RESISTOR
Figure 3. 200mA Output 1.5V to 5V Converter. Lower
Voltage LT1073 Provides Bootstrap Start-Up for LT1170
High Power Switching Regulator
an61fa
AN61-2
Application Note 61
The start-up loop must function over a wide range of
loads and battery voltages. Start-up currents approach
1A, necessitating attention to the LT1073’s saturation and
drive characteristics. The worst case is a nearly depleted
battery and heavy output loading.
MINIMUM INPUT VOLTAGE TO MAINTAIN VOUT = 5V
Figure 4 plots input-output characteristics for the circuit.
Note that the circuit will start into all loads with VBAT =
1.2V. Start-up is possible down to 1.0V at reduced loads.
Once the circuit has started, the plot shows it will drive full
200mA loads down to VBAT = 1.0V. Reduced drive is possible down to VBAT = 0.6V (a very dead battery)! Figure 5
graphs efficiency at two supply voltages over a range of
output currents. Performance is attractive, although at
lower currents circuit quiescent power degrades efficiency.
Fixed junction saturation losses are responsible for lower
overall efficiency at the lower supply voltage.
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
START
RUN
0 20 40 60 80 100 120 140 160 180 200
OUTPUT CURRENT (mA)
100
VOUT = 5V
90
80
EFFICIENCY (%)
The 1.5V powered LT1073 switching regulator forms a
start-up loop. When power is applied the LT1073 runs,
causing its VSW pin to periodically pull current through L1.
L1 responds with high voltage flyback events. These events
are rectified and stored in the 470μF capacitor, producing
the circuits DC output. The output divider string is set up
so the LT1073 turns off when circuit output crosses about
4.5V. Under these conditions the LT1073 obviously can no
longer drive L1, but the LT1170 can. When the start-up
circuit goes off, the LT1170 VIN pin has adequate supply
voltage and can operate. There is some overlap between
start-up loop turn-off and LT1170 turn-on, but it has no
detrimental effect.
VIN = 1.5V
70
60
VIN = 1.2V
50
40
30
20
10
0
0
20 40 60 80 100 120 140 160 180 200
OUTPUT CURRENT (mA)
AN61 F05
Figure 5. Efficiency vs Operating Point for the 1.5V to
5V Converter. Efficiency Suffers at Low Power Because
of Relatively High Quiescent Currents
Low Power 1.5V to 5V Converter
Figure 6, essentially the same approach as the preceding circuit, was developed by Steve Pietkiewicz of LTC.
It is limited to about 150mA output with commensurate
restrictions on start-up current. It’s advantage, good efficiency at relatively low output currents, derives from its
low quiescent power consumption.
The LT1073 provides circuit start-up. When output voltage,
sensed by the LT1073’s “set” input via the resistor divider,
rises high enough Q1 turns on, enabling the LT1302. This
device sees adequate operating voltage and responds by
driving the output to 5V, satisfying its feedback node. The
5V output also causes enough overdrive at the LT1073
feedback pin to shut the device down.
Figure 7 shows maximum permissible load currents for
start-up and running conditions. Performance is quite
good, although the circuit clearly cannot compete with the
previous design. The fundamental difference between the
two circuits is the LT1170’s (Figure 3) much larger power
switch, which is responsible for the higher available power.
Figure 8, however, reveals another difference. The curves
show that Figure 6 is significantly more efficient than the
LT1170 based approach at output currents below 100mA.
This highly desirable characteristic is due to the LT1302’s
much lower quiescent operating currents.
AN61 F04
Figure 4. Input-Output Data for the 1.5V to 5V
Converter Shows Extremely Wide Start-Up and
Running Range into Full Load
an61fa
AN61-3
Application Note 61
L1
3.3μH
D1
5VOUT
10Ω
100k
Q1
2N3906
220Ω
100k
100k
1.5V
CELL
ILIM
VIN
VIN
SW1
SET
SW
+
LT1073
C1
47μF
GND
FB
LT1302
NC
AO
FB
R1
301k
1%
SHDN
SW2
C2
220μF
ILIM
56.2k
1%
20k
4.99k
1%
VC
GND
PGND
+
100pF
0.1μF
0.01μF
C1 = AVX TPSD476M016R0150
C2 = AVX TPSE227M010R0100
36.5k
1%
AN61 F06
L1 = COILCRAFT DO3316-332
D1 = MOTOROLA MBR3130LT3
Figure 6. Single-Cell to 5V Converter Delivers 150mA
with Good Efficiency at Lower Currents
1000
72
68
VIN = 1.5V
66
RUN
100
EFFICIENCY (%)
MAXIMUM LOAD CURRENT (mA )
70
START
10
64
62
VIN = 1.2V
60
58
56
54
52
50
1
0.6
0.8
1.0
1.2 1.4 1.6
INPUT VOLTAGE (V)
1.8
2.0
AN61 F07
Figure 7. Maximum Permissible Loads for Start-Up
and Running Conditions. Allowable Load Current
During Start-Up Is Substantially Less Than Maximum
Running Current.
48
1
10
100
LOAD CURRENT (mA)
1000
AN61 F08
Figure 8. Efficiency Plot for Figure 6. Performance
Is Better Than the Previous Circuit at Lower
Currents, Although Poorer at High Power
an61fa
AN61-4
Application Note 61
Low Power, Low Voltage Cold Cathode Fluorescent
Lamp Power Supply
The Royer converter oscillates at a frequency primarily
set by T1’s characteristics (including its load) and the
0.068μF capacitor. LT1301 driven L1 sets the magnitude of
the Q1-Q2 tail current, hence T1’s drive level. The 1N5817
diode maintains L1’s current flow when the LT1301’s
switch is off. The 0.068μF capacitor combines with T1’s
characteristics to produce sine wave voltage drive at the
Q1 and Q2 collectors. T1 furnishes voltage step-up and
about 1400Vp-p appears at its secondary. Alternating current flows through the 22pF capacitor into the lamp. On
positive half-cycles the lamp’s current is steered to ground
via D1. On negative half-cycles the lamp’s current flows
through Q3’s collector and is filtered by C1. The LT1301’s
ILIM pin acts as a 0V summing point with about 25μA
bias current flowing out of the pin into C1. The LT1301
regulates L1’s current to equalize Q3’s average collector
current, representing 1/2 the lamp current, and R1’s current, represented by VA/R1. C1 smooths all current flow
to DC. When VA is set to zero, the ILIM pin’s bias current
forces about 100μA bulb current.
Most Cold Cathode Fluorescent Lamp (CCFL) circuits
require an input supply of 5V to 30V and are optimized
for bulb currents of 5mA or more. This precludes lower
power operation from 2- or 3-cell batteries often used in
palmtop computers and portable apparatus. A CCFL power
supply that operates from 2V to 6V is detailed in Figure 9.
This circuit, contributed by Steve Pietkiewicz of LTC, can
drive a small CCFL over a 100μA to 2mA range.
The circuit uses an LT1301 micropower DC/DC converter IC
in conjunction with a current driven Royer class converter
comprised of T1, Q1 and Q2. When power and intensity
adjust voltage are applied the LT1301’s ILIM pin is driven
slightly positive, causing maximum switching current
through the IC’s internal switch pin (SW). Current flows
from T1’s center tap, through the transistors, into L1. L1’s
current is deposited in switched fashion to ground by the
regulator’s action.
9
7
22pF
3kV
TI
1
VIN
2V TO 6V
5
4
1Ω
3
2
0.68μF
1N5817
120Ω
CCFL
Q2
ZTX849
Q1
ZTX849
NC
L1
47μH
SELECT
VIN
SW
SENSE
+
LT1301
0.1μF
SHDN
GND
ILIM
PGND
AN61 F09
+ C1
1μF
SHUTDOWN
T1 = COILTRONICS CTX110654-1
L1 = COILCRAFT D03316-473
0.68μF = WIMA MKP-20
10μF
Q3
2N3904
R1
7.5K
1%
D1
1N4148
VA
0V TO 5VDCIN
INTENSITY ADJUST
100μA TO 2mA BULB CURRENT
Figure 9. Low Power Cold Cathode Fluorescent Lamp Supply Is Optimized for Low Voltage Inputs and Small Lamps
an61fa
AN61-5
Application Note 61
Circuit efficiency ranges from 80% to 88% at full load, depending on line voltage. Current mode operation combined
with the Royer’s consistent waveshape vs input results
in excellent line rejection. The circuit has none of the line
rejection problems attributable to the hysteretic voltage
control loops typically found in low voltage micropower
DC/DC converters. This is an especially desirable characteristic for CCFL control, where lamp intensity must remain
constant with shifts in line voltage. Interaction between
the Royer converter, the lamp and the regulation loop is
far more complex than might be supposed, and subject
to a variety of considerations. For detailed discussion see
Reference 3.
Low Voltage Powered LCD Contrast Supply
Figure 10, a companion to the CCFL power supply previously described, is a contrast supply for LCD panels. It
was designed by Steve Pietkiewicz of LTC. The circuit is
noteworthy because it operates from a 1.8V to 6V input,
significantly lower than most designs. In operation the
LT1300/LT1301 switching regulator drives T1 in flyback
VIN
1.8V TO 6V
fashion, causing negative biased step-up at T1’s secondary. D1 provides rectification, and C1 smooths the
output to DC. The resistively divided output is compared
to a command input, which may be DC or PWM, by the
IC’s “ILIM” pin. The IC, forcing the loop to maintain 0V at
the ILIM pin, regulates circuit output in proportion to the
command input.
Efficiency ranges from 77% to 83% as supply voltage
varies from 1.8V to 3V. At the same supply limits, available
output current increases from 12mA to 25mA.
HeNe Laser Power Supply
Helium-Neon lasers, used for a variety of tasks, are difficult loads for a power supply. They typically need almost
10kV to start conduction, although they require only about
1500V to maintain conduction at their specified operating
currents. Powering a laser usually involves some form
of start-up circuitry to generate the initial breakdown
voltage and a separate supply for sustaining conduction.
Figure 11’s circuit considerably simplifies driving the laser.
T1
CONTRAST OUTPUT
VOUT –4V TO –29V
4
1
7
3
150k
10
9
NC
+
VIN
SW
SENSE
SHDN
100μF
NC
LT1300
OR
LT1301
SELECT
PGND
+
8
2
C1
22μF
35V
D1
1N5819
SHUTDOWN
ILIM
GND
12k
+
T1 = DALE LPE-5047-AO45
12k
COMMAND INPUT
PWM OR DC
0% TO 100%
OR 0V TO 5V
2.2μF
AN61 F10
Figure 10. Liquid Crystal Display Contrast Supply Operates from 1.8V to 6V with –4V to –29V Output Range
an61fa
AN61-6
Application Note 61
The start-up and sustaining functions have been combined
into a single, closed-loop current source with over 10kV
of compliance. The circuit is recognizable as a reworked
CCFL power supply with a voltage tripled DC output.2
about 3500V to appear at its secondary. The capacitors and
diodes associated with L1’s secondary form a voltage tripler,
producing over 10kV across the laser. The laser breaks
down and current begins to flow through it. The 47k resistor
limits current and isolates the laser’s load characteristic.
The current flow causes a voltage to appear across the
190Ω resistor. A filtered version of this voltage appears
at the LT1170 FB pin, closing a control loop. The LT1170
adjusts pulse width drive to L2 to maintain the FB pin at
1.23V, regardless of changes in operating conditions. In
this fashion, the laser sees constant current drive, in this
When power is applied, the laser does not conduct and
the voltage across the 190Ω resistor is zero. The LT1170
switching regulator FB pin sees no feedback voltage, and
its switch pin (VSW) provides full duty cycle pulse width
modulation to L2. Current flows from L1’s center tap
through Q1 and Q2 into L2 and the LT1170. This current
flow causes Q1 and Q2 to switch, alternately driving L1.
The 0.47μF capacitor resonates with L1, providing boosted
sine wave drive. L1 provides substantial step-up, causing
Note 2: See References 2 and 3 and this text’s Figure 9.
1800pF
10kV
0.01μF
5kV
47k
5W
1800pF
10kV
11
L1
4
5
8
1
HV DIODES
3
2
0.47μF
+
LASER
2.2μF
Q2
Q1
150Ω
L2
145μH
MUR405
VIN
9V TO 35V
VSW
10k
VIN
+
FB
LT1170
2.2μF
VC
+
0.1μF
190Ω
1%
GND
10k
10μF
1N4002
(ALL)
AN61 F11
VIN
HV DIODES = SEMTECH-FM-50
0.47μF = WIMA 3w 0.15μF TYPE MKP-20
Q1, Q2 = ZETEX ZTX849
L1 = COILTRONICS CTX02-11128-2
L2 = PULSE ENGINEERING PE-92105
LASER = HUGHES 3121H-P
Figure 11. LASER Power Supply Is Essentially A 10,000V Compliance Current Source
an61fa
AN61-7
Application Note 61
case 6.5mA. Other currents are obtainable by varying the
190Ω value. The 1N4002 diode string clamps excessive
voltages when laser conduction first begins, protecting
the LT1170. The 10μF capacitor at the VC pin frequency
compensates the loop and the MUR405 maintains L1’s
current flow when the LT1170 VSW pin is not conducting.
The circuit will start and run the laser over a 9V to 35V
input range with an electrical efficiency of about 80%.
large transformer to generate the 400Hz 95V square wave
required to drive the panel. Figure 12’s circuit, developed
by Steve Pietkiewicz of LTC, eliminates the transformer
by employing an LT1108 micropower DC/DC converter
IC. The device generates a 95VDC potential via L1 and the
diode-capacitor doubler network. The transistors switch
the EL panel between 95V and ground. C1 blocks DC and
R1 allows intensity adjustment. The 400Hz square wave
drive signal can be supplied by the microprocessor or a
simple multivibrator. When compared to conventional EL
panel supplies, this circuit is noteworthy because it can
be built in a square inch with a 0.5 inch height restriction.
Additionally, all components are surface mount types, and
the usual large and heavy 400Hz transformer is eliminated.
Compact Electroluminescent Panel Power Supply
Electroluminescent (EL) panel LCD backlighting presents an
attractive alternative to fluorescent tube (CCFL) backlighting
in some portable systems. EL panels are thin, lightweight,
lower power, require no diffuser and work at lower voltage
than CCFLs. Unfortunately, most EL DC/AC inverters use a
95V
0.1μF
100V
1M
L1
100μH
VIN
2V TO 12V
MMBTA42
+
+
47Ω
33pF
ILIM
C1
1μF
100V
0.1μF
100V
MMBTA42
VIN
SW1
U1
LT1108CS8
MMBTA92
2.26M
EL
PANEL
FB
GND
SW2
30.1k
R1
25k
0.47μF
200V
10k
MMBTA42
400Hz DRIVE
SQUARE WAVE
= MOTOROLA MURS120T3
L1 = COILCRAFT DO3316-104
AN61 F12
Figure 12. Switch Mode EL Panel Driver Eliminates Large 400Hz Transformer
an61fa
AN61-8
Application Note 61
3.3V Powered Barometric Pressure Signal Conditioner
A1’s output biases the LT1172 switching regulator’s operating point, producing a stepped up DC voltage which
appears as T1’s drive and A2’s supply voltage. T1’s return
current out of pin 6 closes a loop back at A1 which is
slaved to the 1.2V reference. This arrangement provides
the required high voltage drive (≈10V) while minimizing
power consumption. This is so because the switching
regulator produces only enough voltage to satisfy T1’s
current requirements. Instrumentation amplifier A2 and A3
provide gain and LTC®1287 A/D converter gives a 12-bit
digital output. A2 is bootstrapped off the transducer supply,
enabling it to accept T1’s common-mode voltage. Circuit
current consumption is about 14mA. If the shutdown pin
is driven high the switching regulator turns off, reducing
The move to 3.3V digital supply voltage creates problems
for analog signal conditioning. In particular, transducer
based circuits often require higher voltage for proper
transducer excitation. DC/DC converters in standard
configurations can address this issue but increase power
consumption. Figure 13’s circuit shows a way to provide
proper transducer excitation for a barometric pressure
sensor while minimizing power requirements.
The 6kΩ transducer T1 requires precisely 1.5mA of excitation, necessitating a relatively high voltage drive. A1
senses T1’s current by monitoring the voltage drop across
the resistor string in T1’s return path.
T1
PRESSURE
TRANSDUCER
≈10V DURING OPERATION
TO PROCESSOR
5
–
10
4
1μF
3.3V
3.3V
A = 10
CLK
A2
LT1101
A3
1/2 LT1078
+
+IN
–
6
DOUT
CS
+
LTC1287
–IN
10k*
0.05μF
GND
1N752
5.6V
VCC
VREF
3.3V
700Ω*
BRIDGE
CURRENT
TRIM
50Ω
BRIDGE
CURRENT
MONITOR
(0.1500V)
100Ω**
1M
CALIB
+
1N4148
22μF
1μF
MUR110
L1
150μH
3.3V
+
2.2μF
100k
–
A1
1/2 LT1078
VSW
VIN
1N4148
VC
LT1172
FB
NC
+
E1
* = 1% FILM RESISTOR
** = 0.1% FILM RESISTOR
L1 = TOKO 262-LYF-0095K
T1 = NOVASENSOR (FREMONT, CA)
NPH-8-100AH
E2
GND
100k
LT1034
1.2V
2N3904
SHUTDOWN
10k
3.3V
AN61 F13
Figure 13. 3.3V Powered, Digital Output, Barometric Pressure Signal Conditioner
an61fa
AN61-9
Application Note 61
total power consumption to about 1mA. In shutdown the
3.3V powered A/D’s output data remains valid. In practice,
the circuit provides a 12-bit representation of ambient
barometric pressure after calibration. To calibrate, adjust
the “bridge current trim” for exactly 0.1500V at the indicated
point. This sets T1’s current to the manufacturers specified point. Next, adjust A3’s trim so that the digital output
corresponds to the known ambient barometric pressure.
If a pressure standard is not available the transducer is
supplied with individual calibration data, permitting circuit
calibration.
Single Cell Barometers
It is possible to power these circuits from a single cell without sacrificing performance. Figure 15, a direct extension
of the above approaches, simply substitutes a switching
regulator that will run from a single 1.5V battery. In other
respects loop action is nearly identical.
Figure 16, also a 1.5V powered design, is related but
eliminates the instrumentation amplifier. As before, the
6kΩ transducer T1 requires precisely 1.5mA of excitation,
necessitating a relatively high voltage drive. A1’s positive
input senses T1’s current by monitoring the voltage drop
across the resistor string in T1’s return path. A1’s negative
input is fixed by the 1.2V LT1004 reference. A1’s output
biases the 1.5V powered LT1110 switching regulator. The
LT1110’s switching produces two outputs from L1. Pin 4’s
rectified and filtered output powers A1 and T1. A1’s output,
Some applications may require operation over a wider
supply range and/or a calibrated analog output. Figure 14’s
circuit is quite similar, except that the A/D converter is
eliminated and a 2.7V to 7V supply is acceptable. The
calibration procedure is identical, except that A3’s analog
output is monitored.
5
T1
–
10
4
A = 10
A2
LT1101
+
+
A3
1/2 LT1078
–
6
20k*
1.500mA
+
10k*
700Ω*
BRIDGE
CURRENT
TRIM
OUTPUT
0V TO 3.100V =
0 TO 31.00" Hg.
OUTPUT
TRIM
3.3V
22μF
MUR110
1k
L1
150μH
50Ω
1μF
3.3V
100Ω
0.1%
+
2.2μF
100k
–
A1
1/2 LT1078
* = 1% FILM RESISTOR
L1 = TOKO 262-LYF-0095K
T1 = NOVASENSOR NPH-8-100AH
VIN
VSW
1N4148
VC
LT1172
NC
FB
+
E1
E2
GND
10k
3.3V
LT1034
1.2V
AN61 F13
Figure 14. Single Supply Barometric Pressure Signal Conditioner Operates Over a 2.7V to 7V Range
an61fa
AN61-10
Application Note 61
T1
5
10
4
A =10
–
A2
LT1101
+
6
OUTPUT
0 TO 3.100V=
0 TO 31.00"Hg
A3
LT1078
+
–
200k*
100k*
10k
CAL
1.5V
AA CELL
+
A1
1/2 LT1078
700Ω
1%
+
150
1μF
–
VIN
50Ω
TRIM FOR
150mV AT
POINT “A”
100k
LT1004-1.2
1N5818
SW1
+
LT1110
10k
NC
100Ω
0.1%
100Ω
IL
FB
A
L1
50μH
SET
GND
150μF
AO
NC
SW2
100k
* = 1% FILM RESISTOR
L1 = COILTRONICS CTX50-1
T1 = NOVASENSOR NPH-8-100AH
AN61 F15
Figure 15. 1.5V Powered Barometric Pressure Signal Conditioner Uses
Instrumentation Amplifier and Voltage Boosted Current Loop
in turn, closes a feedback loop at the regulator. This loop
generates whatever voltage step-up is required to force
precisely 1.5mA through T1. This arrangement provides
the required high voltage drive while minimizing power
consumption. This occurs because the switching regulator produces only enough voltage to satisfy T1’s current
requirements.
L1 pins 1 and 2 source a boosted, fully floating voltage,
which is rectified and filtered. This potential powers A2.
Because A2 floats with respect to T1, it can look differentially across T1’s outputs, pins 10 and 4. In practice,
pin 10 becomes “ground” and A2 measures pin 4’s output
with respect to this point. A2’s gain-scaled output is the
circuit’s output, conveniently scaled at 3.000V = 30.00"Hg.
A2’s floating drive eliminates the requirement for an
instrumentation amplifier, saving cost, power, space and
error contribution.
To calibrate the circuit, adjust R1 for 150mV across the
100Ω resistor in T1’s return path. This sets T1’s current
to the manufacturer’s specified calibration point. Next,
adjust R2 at a scale factor of 3.000V = 30.00"Hg. If R2
cannot capture the calibration, reselect the 200k resistor
in series with it. If a pressure standard is not available,
the transducer is supplied with individual calibration data,
permitting circuit calibration.
This circuit, compared to a high-order pressure standard,
maintained 0.01"Hg accuracy over months with widely
varying ambient pressure shifts. Changes in pressure,
particularly rapid ones, correlated quite nicely to changing
weather conditions. Additionally, because 0.01"Hg corresponds to about 10 feet of altitude at sea level, driving over
hills and freeway overpasses becomes quite interesting.
an61fa
AN61-11
AN61-12
A2
A1
LT1004-1.2
100k
6
5
–
+
100k
4
A1
LT1077
1N4148
0.1μF
1μF
6
8
A2
LT1077
7
3
L1
10k
1%
+
100μF
200k*
1%
4
1
R2
1k
39k
430k
1N5818
1N4148
100Ω
0V TO 3.100V =
OUTPUT 0 TO 31.00"Hg.
L1 = COILTRONICS CTX50-1
4
3
2
SET
SW1
1
5
IL
SW2
LT1110
150Ω
GND
AO
FB
2
0.1μF
VIN
FREMONT, CA (510) 490-9100
† = LUCAS NOVASENSOR
+
–
+
Figure 16. 1.5V Powered Barometric Pressure Signal Conditioner Floats Bridge Drive to
Eliminate Instrumentation Amplifier. Voltage Boosted Current Loop Drives Transducer
AA CELL
100k
1μF
NON-POLAR
68k
* = NOMINAL VALUE. EACH SENSOR REQUIRES SELECTION
** = TRIM FOR 150mV ACROSS A1-A2
100Ω
0.1%
R1**
50Ω
698Ω
1%
10
T1
NOVASENSOR
NPH-8-100AH†
+
AN61 F16
390μF
16V
NICHICON
PL
100Ω
Application Note 61
an61fa
Application Note 61
Until recently, this type of accuracy and stability has only
been attainable with bonded strain gauge and capacitivelybased transducers, which are quite expensive. As such,
semiconductor pressure transducer manufacturers whose
products perform at the levels reported are to be applauded.
Although high quality semiconductor transducers are still
not comparable to more mature technologies, their cost
is low and they are vastly improved over earlier devices.
mode. The crystal and discrete components combine
with the IC’s inverting gain to form a Pierce type oscillator. The LTC485’s differential line driving outputs provide
frequency coded temperature data to a 1000-foot cable
run. A second RS485 transceiver differentially receives
the data and presents a single-ended output. Accuracy
depends on the grade of quartz sensor specified, with 1°C
over 0°C to 100°C achievable.
The circuit pulls 14mA from the battery, allowing about
250 hours operation from one D cell.
Ultra-Low Noise and Low Drift Chopped-FET Amplifier
Quartz Crystal-Based Thermometer
Although quartz crystals have been utilized as temperature sensors (see Reference 5), there has been almost no
widespread adaptation of this technology. This is primarily
due to the lack of standard product quartz-based temperature sensors. The advantages of quartz-based sensors
include simple signal conditioning, good stability and a
direct, noise immune digital output almost ideally suited
to remote sensing.
Figure 17 utilizes an economical, commercially available
(see Reference 6) quartz-based temperature sensor in a
thermometer scheme suited to remote data collection.
The LTC485 RS485 transceiver is set up in the transmit
5V
10M
1000 FEET
TWISTED-PAIR
6
6
4
LTC485
7
3
2
8
5
1
100k
NC
5V
8
OUT
LTC485
1
4
7
3
100Ω
5
NC
2
0°C TO 100°C
= 261.900kHz
– 262.800kHz
Y1
+33.5ppm/°C
10pF
15pF
Y1 = MICRO CRYSTAL (SWISS)
MT1/33.5ppm/°C
0°C = 261.900kHz
100°C = 262.800kHz
Figure 17. Quartz Crystal Based Circuit Provides
Temperature-to-Frequency Conversion. RS485
Transceivers Allow Remote Sensing
"/t'
Figure 18’s circuit combines the extremely low drift of
a chopper-stabilized amplifier with a pair of low noise
FETs. The result is an amplifier with 0.05μV/°C drift, offset
within 5μV, 100pA bias current and 50nV noise in a 0.1Hz
to 10Hz bandwidth. The noise performance is especially
noteworthy; it is almost 35 times better than monolithic
chopper-stabilized amplifiers and equals the best bipolar
types.
FETs Q1 and Q2 differentially feed A2 to form a simple
low noise op amp. Feedback, provided by R1 and R2,
sets closed-loop gain (in this case 10,000) in the usual
fashion. Although Q1 and Q2 have extraordinarily low noise
characteristics, their offset and drift are uncontrolled. A1,
a chopper-stabilized amplifier, corrects these deficiencies.
It does this by measuring the difference between the
amplifier’s inputs and adjusting Q1’s channel current via
Q3 to minimize the difference. Q1’s skewed drain values
ensure that A1 will be able to capture the offset. A1 and
Q3 supply whatever current is required into Q1’s channel to force offset within 5μV. Additionally, A1’s low bias
current does not appreciably add to the overall 100pA
amplifier bias current. As shown, the amplifier is set up
for a noninverting gain of 10,000 although other gains
and inverting operation are possible. Figure 19 is a plot
of the measured noise performance.
The FETs’ VGS can vary over a 4:1 range. Because of this,
they must be selected for 10% VGS matching. This matching allows A1 to capture the offset without introducing
any significant noise.
an61fa
AN61-13
Application Note 61
15V
+
0.02μF
A1
LTC1150
10k
–
Q3
2N2907
–15V
–15V
0.02μF
100k
15V
200Ω*
1k*
450Ω*
900Ω*
–
100k
A2
LT1097
OUTPUT
+
5
+ INPUT
Q2
Q1
* = 1% FILM RESISTOR
Q1, Q2 = 2SK147 TOSHIBA
750Ω*
OPTIONAL
OVER
COMPENSATION
– INPUT
R1
100k
R2
10 Ω
–15V
AN61 F18
Figure 18. Chopper-Stabilized FET Pair Combines Low Bias, Offset and Drift with 45nV Noise
100
NANOVOLTS
AN61 F19
10 SECONDS
Figure 19. Figure 18’s 45nV Noise Performance in a 0.1Hz to 10Hz Bandwidth.
A1’s Low Offset and Drift Are Retained, But Noise Is Almost 35 Times Better
an61fa
AN61-14
Application Note 61
Figure 20 shows the response (trace B) to a 1mV input
step (trace A). The output is clean, with no overshoots or
uncontrolled components. If A2 is replaced with a faster
device (e.g., LT1055) speed increases by an order of
magnitude with similar damping. A2’s optional overcompensation can be used (capacitor to ground) to optimize
response for low closed-loop gains.
A = 500μV/DIV
B = 5V/DIV
100μs/DIV
AN61 F20
Figure 20. Step Response for the Low Noise × 10,000
Amplifier. A 10× Speed Increase Is Obtainable by
Replacing A2 with a Faster Device
High Speed Adaptive Trigger Circuit
Line receivers often require an adaptive trigger to compensate for variations in signal amplitude and DC offsets. The
circuit in Figure 21 triggers on 2mV to 100mV signals from
100Hz to 10MHz while operating from a single 5V rail. A1,
operating at a gain of 20, provides wideband AC gain. The
output of this stage biases a 2-way peak detector (Q1-Q4).
The maximum peak is stored in Q2’s emitter capacitor,
while the minimum excursion is retained in Q4’s emitter
capacitor. The DC value of A1’s output signal’s midpoint
appears at the junction of the 500pF capacitor and the
10MΩ units. This point always sits midway between the
signal’s excursions, regardless of absolute amplitude. This
signal-adaptive voltage is buffered by A2 to set the trigger
voltage at the LT1116’s positive input. The LT1116’s negative input is biased directly from A1’s output. The LT1116’s
output, the circuit’s output, is unaffected by 50:1 signal
amplitude variations. Bandwidth limiting in A1 does not
affect triggering because the adaptive trigger threshold
varies ratiometrically to maintain circuit output.
Split supply versions of this circuit can achieve bandwidths to 50MHz with wider input operating range (See
Reference 7).
5V
3k
Q1
Q2
5V
5V
+
0.005μF
500pF
10M
A1
LT1192
+
–
0.005μF
10M
A2
LT1006
–
2k
5V
1k
750Ω
Q4
Q3
50Ω
+
+
10μF
0.01μF
INPUT
5V
500Ω
3k
+
C1
100μF
C2
0.1μF
500Ω
1N4148
1N4148
Q
LT1116
0.1μF
–
Q
TRIGGER
OUT
NPN = 2N3904
PNP = 2N3906
AN61 F21
Figure 21. Fast Single Supply Adaptive Trigger. Output Comparator’s Trip Level Varies Ratiometrically
with Input Amplitude, Maintaining Data Integrity Over 50:1 Input Amplitude Range
an61fa
AN61-15
Application Note 61
Wideband, Thermally-Based RMS/DC Converter
Applications such as wideband RMS voltmeters, RF leveling
loops, wideband AGC, high crest factor measurements,
SCR power monitoring and high frequency noise measurements require wideband, true RMS/DC conversion.
The thermal conversion method achieves vastly higher
bandwidth than any other approach. Thermal RMS/DC
converters are direct acting, thermoelectronic analog
computers. The thermal technique is explicit, relying on
“first principles,” e.g,. a waveforms RMS value is defined
as its heating value in a load.
Figure 22 is a wideband, thermally-based RMS/DC converter.3 It provides a true RMS/DC conversion from DC
to 10MHz with less than 1% error, regardless of input
signal waveshape. It also features high input impedance
and overload protection.
The circuit consists of three blocks; a wideband FET input
amplifier, the RMS/DC converter and overload protection.
The amplifier provides high input impedance, gain and
drives the RMS/DC converters input heater. Input resistance
is defined by the 1M resistor with input capacitance about
3pF. Q1 and Q2 constitute a simple, high speed FET input
buffer. Q1 functions as a source follower, with the Q2 current source load setting the drain-source channel current.
The LT1206 provides a flat 10MHz bandwidth gain of ten.
Normally, this open-loop configuration would be quite drifty
because there is no DC feedback. The LT1097 contributes
this function to stabilize the circuit. It does this by comparing the filtered circuit output to a similarly filtered version
of the input signal. The amplified difference between these
signals is used to set Q2’s bias, and hence Q1’s channel
current. This forces Q1’s VGS to whatever voltage is required to match the circuit’s input and output potentials.
The capacitor at A1 provides stable loop compensation.
The RC network in A1’s output prevents it from seeing
high speed edges coupled through Q2’s collector-base
junction. Q4, Q5 and Q6 form a low leakage clamp which
precludes A1 loop latch-up during start-up or overdrive
conditions. This can occur if Q1 ever forward biases. The
5k-50pF network gives A2 a slight peaking characteristic at
the highest frequencies, allowing 1% flatness to 10MHz.
A2’s output drives the RMS/DC converter.
The LT1088 based RMS/DC converter is made up of
matched pairs of heaters and diodes and a control amplifier.
The LT1206 drives R1, producing heat which lowers D1’s
voltage. Differentially connected A3 responds by driving
R2, via Q3, to heat D2, closing a loop around the amplifier. Because the diodes and heater resistors are matched,
A3’s DC output is related to the RMS value of the input,
regardless of input frequency or waveshape. In practice,
residual LT1088 mismatches necessitate a gain trim, which
is implemented at A4. A4’s output is the circuit output. The
LT1004 and associated components frequency compensate
the loop and provide good settling time over wide ranges
of operating conditions (see Footnote 3).
Start-up or input overdrive can cause A2 to deliver excessive current to the LT1088 with resultant damage. C1
and C2 prevent this. Overdrive forces D1’s voltage to an
abnormally low potential. C1 triggers low under these
conditions, pulling C2’s input low. This causes C2’s output
to go high, putting A2 into shutdown and terminating the
overload. After a time determined by the RC at C2’s input,
A2 will be enabled. If the overload condition still exists the
loop will almost immediately shut A2 down again. This
oscillatory action will continue, protecting the LT1088 until
the overload condition is removed.
Note 3: Thermally based RMS/DC conversion is detailed in Reference 9.
an61fa
AN61-16
1M
10M
330pF
3k
0.01
–
A1
LT1097
+
Q6
Q5
Q4
10k
2N3904s
0.1
10MHz
TRIM
0.1
10M
50pF
5k
–
–15V
0.1μF
OVERLOAD TRIM. SET AT
10% BELOW D1's VOLTAGE
WITH CIRCUIT OPERATING
AT FULL SCALE
100Ω*
SD 900Ω*
A2
LT1206
+
15V
1
–
10k
13
D1
LT1004
1.2V
2k
1k
1N914
6
D2
5
10k
0.1
–15V
+
4.7k
15V
9.09M*
+
15V
+
Q3
2N2219
1k
LT10041.2V
9.09M*
15V
–
A4
1/2 LT1013
AN61 F22
24k
A3
1/2 LT1013
–
10k
FULL-SCALE
TRIM
C2
1/2 LT1018
–
8
10
0.01μF
1k*
1k*
250Ω
R2
2.7k*
510k
15V
LT1088
15V
15V
250Ω
R1
C1
1/2 LT1018
+
14
7
3
12
2.7k*
500Ω
15V
Figure 22. Complete 10MHz Thermally-Based RMS/DC Converter Has 1% Accuracy, High Input Impedance and Overload Protection
* = 1% FILM RESISTOR
–15V
330Ω
Q2
2N3904
Q1
2N5486
0 – 1VRMS
DC –10MHz 15V
0.01μF
ZERO TRIM
(TRIM AT 10% OF
FULL-SCALE)
0.022μF
3300pF
1.5M
VOUT
10k*
10k*
3k
1k
Application Note 61
an61fa
AN61-17
Application Note 61
Performance for the circuit is quite impressive. Figure 23
plots error from DC to 11MHz. The graph shows 1% error
bandwidth of 11MHz. The slight peaking out to 5MHz is
due to the gain boost network at A2’s negative input. The
peaking is minimal compared to the total error envelope,
and a small price to pay to get the 1% accuracy to 10MHz.
To trim this circuit put the 5kΩ potentiometer at its
maximum resistance position and apply a 100mV, 5MHz
signal. Trim the 500Ω adjustment for exactly 1VOUT. Next,
apply a 5MHz 1V input and trim the 10k potentiometer for
10.00VOUT. Finally, put in 1V at 10MHz and adjust the 5kΩ
trimmer for 10.00VOUT. Repeat this sequence until circuit
output is within 1% accuracy for DC-10MHz inputs. Two
passes should be sufficient.
It is worth considering that this circuit performs the same
function as instruments costing thousands of dollars.4
ERROR (%)
1
0
0.7% ERROR AT 10MHz
–1
0
1
2
3
4 5 6 7 8
FREQUENCY (MHz)
9 10 11
AN61 F23
Figure 23. Error Plot for the RMS/DC Converter.
Frequency Dependent Gain Boost at A2 Preserves 1%
Accuracy, But Causes Slight Peaking Before Roll-Off
Hall Effect Stabilized Current Transformer
Current transformers are common and convenient. They
permit wideband current measurement independent
of common-mode voltage considerations. The most
Note 4: Viewed from a historical perspective it is remarkable that so much
precision wideband performance is available from such a relatively simple
configuration. For perspective, see Appendix A, “Precision Wideband
Circuitry . . . Then and Now.”
convenient current transformers are the “clip-on” type,
commercially sold as “current probes.” A problem with
all simple current transformers is that they cannot sense
DC and low frequency information. This problem was addressed in the mid-1960’s with the advent of the Hall effect
stabilized current probe. This approach uses a Hall effect
device within the transformer core to sense DC and low
frequency signals. This information is combined with the
current transformers output to form a composite DC-tohigh frequency output. Careful roll-off and gain matching
of the two channels preserves amplitude accuracy at all
frequencies.5 Additionally, the low frequency channel
is operated as a “force-balance,” meaning that the low
frequency amplifier’s output is fed back to magnetically
bias the transformer flux to zero. Thus, the Hall effect
device does not have to respond linearly over wide ranges
of current and the transformer core never sees DC bias,
both advantageous conditions. The amount of DC and
low frequency information is obtained at the amplifier’s
output, which corresponds to the bias needed to offset
the measured current.
Figure 24 shows a practical circuit. The Hall effect transducer lies within the core of the clip-on current transformer
specified. A very simplistic way to model the Hall generator is as a bridge, excited by the two 619Ω resistors. The
Hall generator’s outputs (the midpoints of the “bridge”)
feed differential input transconductance amplifier A1,
which takes gain, with roll-off set by the 50Ω, 0.02μF RC
at its output. Further gain is provided by A2, in the same
package as A1. A current buffer provides power gain to
drive the current transformers secondary. This connection
closes a flux nulling loop in the transducer core. The offset
adjustments should be set for 0V output with no current
flowing in the clip-on transducer. Similarly, the loop gain
and bandwidth trims should be set so that the composite
output (the combined high and low frequency output across
the grounded 50Ω resistor) has clean step response and
correct amplitude from DC to high frequency.
Note 5: Details of this scheme are nicely presented in Reference 15.
Additional relevant commentary on parallel path schemes appears in
Reference 7.
an61fa
AN61-18
Application Note 61
+16V
619Ω
(TYPICAL)
DC AND LOW FREQUENCY OUTPUT
CONCEPTUAL MODEL
OF HALL EFFECT
SENSOR-XFORMER.
TEKTRONIX
120-0464-00 OR
120-0464-02
COMPOSITE OUTPUT TO OPTIONAL
ATTENUATOR AND WIDEBAND AMPLIFIER
+16V
10μH
10μH
3
2
+
A1
OTA
LT1228
–
5
DIFFERENTIAL
HALL SENSOR
AMPLIFIER
CURRENT
CARRYING
CONDUCTOR
AND
RESULTANT
FIELD
50Ω
7
1
50Ω
BANDWIDTH
ISET
2k
8
330Ω
0.02
(TYPICAL)
X1
CURRENT
BUFFER
+
A2
CFA
LT1228
–
6
4
200Ω
20k
LOOP GAIN
–16
4.7k
A1, A2 = LT1228 DUAL
16Ω
1k
619Ω
(TYPICAL)
+16V
–16V
1k
–16V
1k
OFFSET
TRIM
100Ω
OFFSET
ADJ.
1k
OFFSET
TRIM
1k
AN62 TA24
Figure 24. Hall Effect Stabilized Current Transformer (DC → High Frequency Current Probe)
Figure 25 shows a practical way to conveniently evaluate
this circuits performance. This partial schematic of the
Tektronix P-6042 current probe shows a similar signal
conditioning scheme for the transducer specified in
Figure 24. In this case Q22, Q24 and Q29 combine with
differential stage M-18 to form the Hall amplifier. To evaluate Figure 24’s circuit remove M-18, Q22, Q24 and Q29.
Next, connect LT1228 pins 3 and 2 to the former M-18
pins 2 and 10 points, respectively. The ±16V supplies are
available from the P-6042’s power bus. Also, connect the
right end of Figure 24’s 200Ω resistor to what was Q29’s
collector node. Finally, perform the offset, loop gain and
bandwidth trims as previously described.
an61fa
AN61-19
Figure reproduced with permission
of Tektronix, Inc.
AN61-20
Figure 25. Tektronix P-6042 Hall Effect Based Current Probe Servo Loop.
Figure 24 Replaces M18 Amplifier and Q22, Q24 and Q29
AN61 F25
TO
WIDEBAND
AMPLIFIER
SECTION
Application Note 61
an61fa
Application Note 61
Triggered 250 Picosecond Rise Time Pulse Generator
Verifying the rise time limit of wideband test equipment
setups is a difficult task. In particular, the “end-to-end”
rise time of oscilloscope-probe combinations is often
required to assure measurement integrity. Conceptually,
a pulse generator with rise times substantially faster than
the oscilloscope-probe combination can provide this
information. Figure 26’s circuit does this, providing an
800ps pulse with rise and fall times inside 250ps. Pulse
amplitude is 10V with a 50Ω source impedance. This
circuit has similarities to a previously published design
(see Reference 7) except that it is triggered instead of free
running. This feature permits synchronization to a clock or
other event. The output phase with respect to the trigger
is variable from 200ps to 5ns.
The pulse generator requires high voltage bias for operation. The LT1082 switching regulator to forms a high
voltage switched mode control loop. The LT1082 pulse
5V
+
L1
820μH
1μF
MUR120
10k
+
+
2μF
430k
VIN
R3
1M
12k
LT1082
Figure 27 shows waveforms. A 3.9GHz sampling oscilloscope (Tektronix 661 with 4S2 sampling pug-in) measures
the pulse (trace B) at 10V high with an 800ps base. Rise
time is 250ps, with fall time indicating 200ps. The times
are probably slightly faster, as the oscilloscope’s 90ps rise
time influences the measurement.7 The input trigger pulse
is trace A. Its amplitude provides a convenient way to vary
the delay time between the trigger and output pulses. A
1V to 5V amplitude setting produces a continuous 5ns to
200ps delay range.
AVALANCHE BIAS
TYPICALLY 70V.
(SEE TEXT)
FB
E2
The high voltage is applied to Q1, a 40V breakdown device,
via the R3-C1 combination. The high voltage “bias adjust”
control should be set at the point where free running
pulses across R4 just disappear. This puts Q1 slightly
below its avalanche point. When an input trigger pulse
is applied Q1 avalanches. The result is a quickly rising,
very fast pulse across R4. C1 discharges, Q1’s collector
voltage falls and breakdown ceases. C1 then recharges to
just below the avalanche point. At the next trigger pulse
this action repeats.6
1μF
500k
BIAS ADJUST
VSW
width modulates at its 40kHz clock rate. L1’s inductive
events are rectified and stored in the 2μF output capacitor.
The adjustable resistor divider provides feedback to the
LT1082. The 10k-1μF RC provides noise filtering.
E1
GND
VC
+
C1
2pF
2μF
A = 0.5V/DIV
B = 1V/DIV
(UNCALIBRATED)
TRIGGER INPUT
TRISE = 10NS OR
LESS. 1V TO 5V
(SEE TEXT)
50kHz MAXIMUM
5pF
L2
Q1
2N2369 (SEE TEXT)
OUTPUT
C2
3pF TO 12pF
50Ω
10k
R4
50Ω
L1 = J.W. MILLER # 100267
L2 = 1 TURN # 28 WIRE, 1/4" TOTAL LENGTH
Figure 26. Triggered 250ps Rise Time Pulse Generator.
Trigger Pulse Amplitude Controls Output Phase
AN62 F26
100 PICOSECONDS/DIV
AN61 F27
Figure 27. Input Pulse Edge (Trace A) Triggers the
Avalanche Pulse Output (Trace B). Display Granularity Is
Characteristic of Sampling Oscilloscope Operation
Note 6: This circuit is based on the operation of the Tektronix Type 111
Pulse Generator. See Reference 16.
Note 7: I’m sorry, but 3.9GHz is the fastest ’scope in my house (as of
September, 1993).
an61fa
AN61-21
Application Note 61
Some special considerations are required to optimize
circuit performance. L2’s very small inductance combines
with C2 to slightly retard the trigger pulse’s rise time. This
prevents significant trigger pulse artifacts from appearing
at the circuit’s output. C2 should be adjusted for the best
compromise between output pulse rise time and purity.
Figure 28 shows partial pulse rise with C2 properly adjusted. There are no discernible discontinuities related to
the trigger event.
usually mandate a separate 12V supply and pulse forming
circuitry. Figure 29’s circuit provides the complete flash
memory programming function with a single IC and some
discrete components. All components are surface mount
types, so little board space is required. The entire function
runs off a single 5V supply.
MBRS130T3
(MOTOROLA)
L1
33μH
SWITCH
5V
VIN
LT1109-12
SHDN
SENSE
GND
0.2V/DIV
1 = FLASH PROGRAM
0 = STANDBY
VPP FLASH VOUT
12V
60mA
+
33μF
L1 = SUMIDA CD54-330
"/t'
Figure 29. Switching Regulator Provides Complete
Flash Memory Programmer
500 PICOSECONDS/DIV
AN61 F28
Figure 28. Expanded Scale View of Leading Edge Is
Clean with No Trigger Pulse Artifacts. Display Granularity
Derives from Sampling Oscilloscope Operation
Q1 may require selection to get avalanche behavior. Such
behavior, while characteristic of the device specified, is not
guaranteed by the manufacturer. A sample of 50 Motorola
2N2369s, spread over a 12 year date code span, yielded
82%. All “good” devices switched in less than 600ps. C1
is selected for a 10V amplitude output. Value spread is
typically 2pF to 4pF. Ground plane type construction with
high speed layout, connection and termination techniques
are essential for a good results from this circuit.
Flash Memory Programmer
Although “Flash” type memory is increasingly popular,
it does require some special programming features. The
5V powered memories need a carefully controlled 12V
“VPP” programming pulse. The pulse’s amplitude must
be within 5% to assure proper operation. Additionally, the
pulse must not overshoot, as memory destruction may
occur for VPP outputs above 14V.8 These requirements
The LT1109-12 switching regulator functions by repetitively pulsing L1. L1 responds with high voltage flyback
events, which are rectified by the diode and stored in the
10μF capacitor. The “sense” pin provides feedback, and
the output voltage stabilizes at 12V within a few percent.
The regulator’s “shutdown” pin provides a way to control
the VPP programming voltage output. With a logical
zero applied to the pin the regulator shuts down, and no
VPP programming voltage appears at the output. When
the pin goes high (trace A, Figure 30) the regulator is
activated, producing a cleanly rising, controlled pulse at
the output (trace B). When the pin is returned to logical
zero, the output smoothly decays off. The switched mode
delivery of power combined with the output capacitor’s
filtering prevents overshoot while providing the required
pulse amplitude accuracy. Trace C, a time and amplitude
expanded version of trace B, shows this. The output
steps up in amplitude each time L1 dumps energy into
the output capacitor. When the regulation point is reached
the amplitude cleanly flattens out, with only about 75mV
of regulator ripple.
Note 8: See Reference 17 for detailed discussion.
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AN61-22
Application Note 61
3.3VIN
2
A = 5V/DIV
6
5
4
LTC1043
fOUT
0kHz TO
3kHz
17
B = 5V/DIV
22k
8
7
11
+
C = 0.1V/DIV
LT1034
1.2V
22μF
C1**
0.01
μF
12
A, B = 1ms/DIV
C = 50μs/DIV
14
13
AN61 F30
Figure 30. Flash Memory Programmer Waveforms Show
Controlled Edges. Trace C Details Rise Time Settling
3.3V Powered V/F Converter
Figure 31 is a “charge pump” type V/F converter specifically designed to run from a 3.3V rail.9 A 0V to 2V input
produces a corresponding 0kHz to 3kHz output with
linearity inside 0.05%. To understand how the circuit
works assume that A1’s negative input is just below 0V.
The amplifier output is positive. Under these conditions,
LTC1043’s pins 12 and 13 are shorted as are pins 11 and 7,
allowing the 0.01μF capacitor (C1) to charge to the 1.2V
LT1034 reference. When the input-voltage-derived current ramps A1’s summing point (negative input-trace A,
Figure 32) positive, its output (trace B) goes low. This
reverses the LTC1043’s switch states, connecting pins
12 and 14, and 11 and 8. This effectively connects C1’s
positively charged end to ground on pin 8, forcing current
to flow from A1’s summing junction into C1 via LTC1043
pin 14 (pin 14’s current is trace C). This action resets A1’s
summing point to a small negative potential (again, trace
A). The 120pF-50k-10k time constant at A1’s positive input
ensures A1 remains low long enough for C1 to completely
discharge (A1’s positive input is trace D). The Schottky
diode prevents excessive negative excursions due to the
120pF capacitors differentiated response.
When the 120pF positive feedback path decays, A1’s
output returns positive and the entire cycle repeats. The
oscillation frequency of this action is directly related to
the input voltage.
16
10k
FULL SCALE
TRIM
INPUT
0V TO
2V
3.3VIN
75k*
–
1μF
A1
1/2 LT1017
+
1N5712
D1
1N4148
C2
560pF
120pF
1.6M
(10Hz TRIM)
50k
AN61 F31
10k
* = 1% FILM RESISTOR, TYPE TRW-MTR+120ppm/°C
** = POLYSTYRENE
Figure 31. 3.3V Powered Voltage-to-Frequency Converter.
Charge Pump Based Feedback Maintains High Linearity
and Stability
A = 0.02V/DIV
B = 2V/DIV
C = 5mA/DIV
D = 2V/DIV
50μs/DIV
AN61 F32
Figure 32. Waveform for the 3.3V Powered V/F. Charge
Pump Action (Trace C) Maintains Summing Point (Trace A),
Enforcing High Linearity and Accuracy
Note 9: See Reference 20 for a survey of V/F techniques. The circuit
shown here is derived from Figure 8 in LTC Application Note 50,
“Interfacing to Microprocessor Based 5V Systems” by Thomas Mosteller.
This is an AC coupled feedback loop. Because of this,
start-up or overdrive conditions could force A1 to go low
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AN61-23
Application Note 61
and stay there. When A1’s output is low the LTC1043’s
internal oscillator sees C2 and will begin oscillation if A1
remains low long enough. This oscillation causes charge
pumping action via the LTC1043-C1-A1 summing junction
path until normal operation commences. During normal
operation A1 is never low long enough for oscillation to
occur, and controls the LTC1043 switch states via D1.
by a standard 1% film resistor. The type called out has a
temperature characteristic that opposes C1’s –120ppm/°C
drift, resulting in the low overall circuit drift noted.
Broadband Random Noise Generator
Filter, audio, and RF-communications testing often require
a random noise source.10 Figure 33’s circuit provides an
RMS-amplitude regulated noise source with selectable
bandwidth. RMS output is 300mV with a 1kHz to 5MHz
bandwidth, selectable in decade ranges.
To calibrate this circuit apply 7mV and select the 1.6M
(nominal) value for 10Hz out. Then apply 2.000V and set
the 10k trim for exactly 3kHz output. Pertinent specifications include linearity of 0.05%, power supply rejection
of 0.04%/V, temperature coefficient of 75ppm/°C of scale
and supply current of about 200μA. The power supply
may vary from 2.6V to 4.0V with no degradation of these
specifications. If degraded temperature coefficients are
acceptable, the film resistor specified may be replaced
Noise source D1 is AC coupled to A2, which provides a
broadband gain of 100. A2’s output feeds a gain control
stage via a simple, selectable lowpass filter. The filter’s
Note 10: See Appendix B, “Symmetrical White Gaussian Noise,” guest
written by Ben Hessen-Schmidt of Noise Com, Inc. for tutorial on noise.
0.1(1kHz)
1μF
16k
+
15V
D1
NC201
1k
0.01(10kHz)
1.6k
A2
LT1226
–
0.001(100kHz)
1k
1k
100pF(1MHz)
10Ω
NC
(5MHz)
15V
+
A3
LT1228
SET
+
–
A4
LT1228
CFA
910Ω
3k
OUTPUT
–
0.1μF
510Ω
1μF
NON POLAR
–15V
15V
–
+
–15V
+
A5
LT1006
22μF
22μF
– –
10k
+
10Ω
0.5μF
10k
1M
4.7k
–15V
NC 201 = NOISE COM CORP.
NOISE COM = (201) 261-8797
1N4148
THERMALLY
COUPLED
LT1004
1.2V
AN61 F33
Figure 33. Broadband Random Noise Generator Uses Gain Control Loop to Enhance Noise Spectrum Amplitude Uniformity
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AN61-24
Application Note 61
output is applied to A3, an LT1228 operational transconductance amplifier. A3’s output feeds LT1228 A4, a current
feedback amplifier. A4’s output, also the circuit’s output, is
sampled by the A5-based gain control configuration. This
closes a gain control loop to A3. A3’s set current controls
gain, allowing overall output level control.
Figure 34 shows noise at 1MHz bandpass, with Figure 35
showing RMS noise versus frequency in the same bandpass. Figure 36 plots similar information at full bandwidth
(5MHz). RMS output is essentially flat to 1.5MHz with
about ±2dB control to 5MHz before sagging badly.
1V/DIV
10μs/DIV
AN61 F34
Figure 34. Figure 33’s Output in the 1MHz Filter Position
12
AMPLITUDE VARIANCE (dB)
9
6
3
0
–3
–6
–9
–12
0
0.1
0.2
0.3
0.4
0.5
0.6
FREQUENCY (MHz)
0.7
0.8
0.9
1.0
AN61 F35
Figure 35. Amplitude vs Frequency for the Random Noise Generator Is Essentially Flat to 1MHz
9
6
AMPLITUDE VARIANCE (dB)
3
0
–3
–6
–9
–12
–15
–18
–21
0
1
2
3
4
5
6
FREQUENCY (MHz)
7
8
9
10
AN61 F36
Figure 36. RMS Noise vs Frequency at 5MHz Bandpass Shows Slight Fall-Off Beyond 1MHz
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AN61-25
Application Note 61
Figure 37’s similar circuit substitutes a standard zener for
the noise source but is more complex and requires a trim.
A1, biased from the LT1004 reference, provides optimum
drive for D1, the noise source. AC coupled A2 takes a
broadband gain of 100. A2’s output feeds a gain-control
stage via a simple selectable lowpass filter. The filter’s output
is applied to LT1228 A3, an operational transconductance
amplifier. A3’s output feeds LT1228 A4, a current feedbacks
amplifier. A4’s output, the circuit’s output, is sampled by
the A5-based gain control configuration. This closes a gain
control loop back at A3. A3’s set input current controls its
gain, allowing overall output level control.
To adjust this circuit, place the filter in the 1kHz position
and trim the 5k potentiometer for maximum negative bias
at A3, pin 5.
1M
0.1μF
15V
100k
2
3
–
1kHz
8
0.01μF
1
A1
1/2 LT1013
+
4
3
+
1μF
–15V
10kHz
1μF
50k
5k
D1
1N753
6.2k
1k
2
1k
+
0.001μF
1.6k
A2
LT1226
100kHz
–
100pF
1MHz
1k
10pF
10Ω
5MHz
15V
3
2
7
+
1
A3
1/2 LT1228
–
5
900Ω
SET
8
+
A4
1/2 LT1228
–
6
4
510Ω
1VP-P
OUTPUT
1μF
NONPOLAR
10k
–15V
3k
22μF
22μF
+
10Ω
+
0.1μF
0.05μF
10k
15V
–
7
A5
1/2 LT1013
6
5
1M
4.7k
–15V
1N4148s
COUPLE THERMALLY
LT1004
1.2V
+
–15V
AN61 F37
Figure 37. A Similar Circuit Uses a Standard Zener Diode, But Is More Complex and Requires Trimming
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AN61-26
Application Note 61
Switchable Output Crystal Oscillator
Figure 38’s simple crystal oscillator circuit permits crystals
to be electronically switched by logic commands. The
circuit is best understood by initially ignoring all crystals.
Further, assume all diodes are shorts and their associated
1k resistors open. The resistors at the LT1116’s positive
input set a DC bias point. The 2k-25pF path sets up phase
shifted feedback and the circuit looks like a wideband unity
gain follower at DC. When “Xtal A” is inserted (remember,
D1 is temporarily shorted) positive feedback occurs and
oscillation commences at the crystals resonant frequency.
If D1 and its associated 1k value are realized, oscillation
can only continue if logic input A is biased high. Similarly,
additional crystal-diode-1k branches permit logic selection
of crystal frequency.
For AT cut crystals about a millisecond is required for
the circuit output to stabilize due to the high Q factors
involved. Crystal frequencies can be as high as 16MHz
before comparator delays preclude reliable operation.
XTAL X
LOGIC INPUTS
RX
DX
XTAL B
AS MANY STAGES
AS DESIRED
1k
B
D2
XTAL A
5V
1k
A
5V
1k
D1
+
OUTPUT
LT1116
1k
–
= 1N4148
2k
GROUND CRYSTAL CASES
Q'
"/t'
Figure 38. Switchable Output Crystal Oscillator. Biasing A
or B High Places the Associated Crystal in the Feedback Path.
Additional Crystal Branches Are Permissible
REFERENCES
1. Williams, Jim and Huffman, Brian. “Some Thoughts
on DC-DC Converters,” pages 13-17, “1.5V to 5V Converters.” Linear Technology Corporation, Application
Note 29, October 1988.
2. Williams, J., “Illumination Circuitry for Liquid Crystal
Displays,” Linear Technology Corporation, Application
Note 49, August 1992.
3. Williams, J., “Techniques for 92% Efficient LCD Illumination,” Linear Technology Corporation, Application
Note 55, August 1993.
4. Williams, J., “Measurement and Control Circuit Collection,” Linear Technology Corporation, Application
Note 45, June 1991.
5. Benjaminson, Albert, “The Linear Quartz Thermometer ––a New Tool for Measuring Absolute and Difference
Temperatures,” Hewlett-Packard Journal, March 1965.
6. Micro Crystal-ETA Fabriques d’Ebauches., “Miniature
Quartz Resonators - MT Series” Data Sheet. 2540
Grenchen, Switzerland.
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AN61-27
Application Note 61
7. Williams, J., “High Speed Amplifier Techniques,” Linear
Technology Corporation, Application Note 47, August
1991.
8. Williams, Jim, “High Speed Comparator Techniques,”
Linear Technology Corporation, Application Note 13,
April 1985.
9. Williams, Jim, “A Monolithic IC for 100MHz RMS-DC
Conversion,” Linear Technology Corporation, Application Note 22, September 1987.
10. Ott, W.E., “A New Technique of Thermal RMS Measurement,” IEEE Journal of Solid State Circuits, December
1974.
11. Williams, J.M. and Longman, T.L., “A 25MHz Thermally
Based RMS-DC Converter,” 1986 IEEE ISSCC Digest
of Technical Papers.
12. O’Neill, P.M., “A Monolithic Thermal Converter,” H.P.
Journal, May 1980.
13. C. Kitchen, L. Counts, “RMS-to-DC Conversion Guide,”
Analog Devices, Inc. 1986.
14. Tektronix, Inc. “P6042 Current Probe Operating and
Service Manual,” 1967.
15. Weber, Joe, “Oscilloscope Probe Circuits,” Tektronix,
Inc., Concept Series. 1969.
16. Tektronix, Inc., Type 111 Pretrigger Pulse Generator
Operating and Service Manual, Tektronix, Inc. 1960.
17. Williams, J., “Linear Circuits for Digital Systems,”
Linear Technology Corporation, Application Note 31,
February 1989.
18. Williams, J., “Applications for a Switched-Capacitor
Instrumentation Building Block,” Linear Technology
Corporation, Application Note 3, July 1985.
19. Williams, J., “Circuit Techniques for Clock Sources,”
Linear Technology Corporation, Application Note 12,
October 1985.
20. Williams, J. “Designs for High Performance Voltageto-Frequency Converters,” Linear Technology Corporation, Application Note 14, March 1986.
APPENDIX A
Precision Wideband Circuitry . . . Then and Now
Text Figure 22’s relatively straightforward design provides
a sensitive, thermally-based RMS/DC conversion to 10MHz
with less than 1% error. Viewed from a historical perspective it is remarkable that so much precision wideband
performance is so easily achieved.
Thirty years ago these specifications presented an extremely
difficult engineering challenge, requiring deep-seated knowledge of fundamentals, extraordinary levels of finesse and
an interdisciplinary outlook to achieve success.
Note 1: We are all constantly harangued about the advances made in
computers since the days of the IBM360. This section gives analog
aficionados a stage for their own bragging rights. Of course, an HP3400A
was much more interesting than an IBM360 in 1965. Similarly, Figure 22’s
The Hewlett-Packard model HP3400A (1965 price
$525 . . . about 1/3 the yearly tuition at M.I.T.) thermallybased RMS voltmeter included all of Figure 22’s elements,
but considerably more effort was required in its execution.1
Our comparative study begins by considering H-P’s version
of Figure 22’s FET buffer and precision wideband amplifier.
The text is taken directly from the HP3400A Operating and
Service Manual.2
capabilities are more impressive than any contemporary computer I’m
aware of.
Note 2: All Hewlett-Packard text and figures used here are copyright 1965
Hewlett-Packard Company. Reproduced with permission.,
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AN61-28
Application Note 61
Copyright 1965 Hewlett-Packard Co.
Reproduced with permission.
Figure A1. The “Impedance Converter Assembly,” H-P’s Equivalent of Figure 22’s Wideband FET Buffer
Note 3: Although JFETs were available in 1965 their performance was
inadequate for this design’s requirements. The only available option was
the Nuvistor triode described.
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AN61-29
Figure A2. The Hewlett-Packard 3400A’s Wideband Input Buffer. Nuvistor Triode (Upper Center) Provided Speed, Low Noise, and High Impedance.
Circuit Required 75V, – 17.5V and –6.3V Supplies. Regulated Filament Supply Stabilized Follower Gain While Minimizing Noise
Application Note 61
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AN61-30
Application Note 61
If that’s not enough to make you propose marriage to
modern high speed monolithic amplifiers, consider the
design heroics spent on the thermal converter.
Copyright 1965 Hewlett-Packard Co.
Reproduced with permission.
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AN61-31
AN61-32
Figure A3. H-P’s Wideband Amplifier, the “Video Amplifier Assembly” Contained DC and AC Feedback Loops,
Peaking Networks, Bootstrap Feedback and Other Subtleties to Equal Figure 22’s Performance
Copyright 1965 Hewlett-Packard Co.
Reproduced with permission.
Application Note 61
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Figure A4. The Voltmeters “Video Amplifier” Received Input at Board’s Left Side. Amplifier Output Drove Shrouded
Thermal Converter at Lower Right. Note High Frequency Response Trimmer Capacitor at Left Center
Application Note 61
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AN61-33
Application Note 61
Copyright 1965 Hewlett-Packard Co.
Reproduced with permission.
Note 4: In 1965 almost all thermal converters utilized matched pairs of
discrete heater resistors and thermocouples. The thermocouples’ low
level output necessitated chopper amplifier signal conditioning, the only
technology then available which could provide the necessary DC stability.
Note 5: The low level chopping technology of the day was mechanical
choppers, a form of relay. H-P’s use of neon lamps and photocells as
microvolt choppers was more reliable and an innovation. Hewlett-Packard
has a long and successful history of using lamps for unintended purposes.
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AN61-34
Figure A5. H-P’s Thermal Converter (“A4”) and Control Amplifier (“A6”) Perform Similarly to Text Figure 22’s Dual
Op Amp and LT1088. Circuit Realization Required Far More Attention to Details
Copyright 1965 Hewlett-Packard Co.
Reproduced with permission.
Application Note 61
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AN61-35
Figure A6. Chopper Amplifier Board Feedback Controlled the Thermal Converter. Over Fifty Components Were Required,
Including Neon Lamps, Photocells and Six Transistors. Photo-Chopper Assembly Is at Board’s Lower Right
Application Note 61
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AN61-36
Figure A7. Figure 22’s Circuit Puts Entire HP3400 Electronics on One Small Board. FET Buffer-LT1206 Amplifier Appear Left Center
Behind BNC Shield. LT1088 IC (Upper Center) Replaces Thermal Converter. LT1013 (Upper Right) Based Circuitry Replaces PhotoChopper Board. LT1018 and Components (Lower Right) Provide Overload Protection. Ain’t Modern ICs Wonderful?
Application Note 61
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AN61-37
Application Note 61
When casually constructing a wideband amplifier with a
few mini-DIPs, the reader will do well to recall the pain
and skill expended by the HP3400A’s designers some 30
years ago.
Incidentally, what were you doing in 1965?
Copyright 1965 Hewlett-Packard Co. Reproduced with permission.
APPENDIX B
Symmetrical White Gaussian Noise
by Ben Hessen-Schmidt,
NOISE COM, INC.
White noise provides instantaneous coverage of all frequencies within a band of interest with a very flat output
spectrum. This makes it useful both as a broadband
stimulus and as a power-level reference.
Symmetrical white Gaussian noise is naturally generated
in resistors. The noise in resistors is due to vibrations of
the conducting electrons and holes, as described by Johnson and Nyquist.1 The distribution of the noise voltage is
symmetrically Gaussian, and the average noise voltage is:
Vn = 2 kT ∫ R(f) p(f) df
(1)
k = 1.38E–23 J/K (Boltzmann’s constant)
T = temperature of the resistor in Kelvin
f=
frequency in Hz
h = 6.62E–34 Js (Planck’s constant)
R(f) = resistance in ohms as a function of frequency
hf
kT [ exp(hf/kT)−1]
Note 1: See “Additional Reading” at end of this section.
Vn2
N=
= kTB
4R
(3)
where the “4” results from the fact that only half of the
noise voltage and hence only 1/4 of the noise power is
delivered to a matched load.
Equation 3 shows that the available noise power is proportional to the temperature of the resistor; thus it is often
called thermal noise power, Equation 3 also shows that
white noise power is proportional to the bandwidth.
Where:
p(f) =
p(f) is close to unity for frequencies below 40GHz when
T is equal to 290°K. The resistance is often assumed to
be independent of frequency, and ∫df is equal to the noise
bandwidth (B). The available noise power is obtained when
the load is a conjugate match to the resistor, and it is:
(2)
An important source of symmetrical white Gaussian noise
is the noise diode. A good noise diode generates a high
level of symmetrical white Gaussian noise. The level is
often specified in terms of excess noise ratio (ENR).
ENR (in dB) =10Log
( Te − 290)
290
(4)
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AN61-38
Application Note 61
Te is the physical temperature that a load (with the same
impedance as the noise diode) must be at to generate the
same amount of noise.
The ENR expresses how many times the effective noise
power delivered to a non-emitting, nonreflecting load
exceeds the noise power available from a load held at the
reference temperature of 290°K (16.8°C or 62.3°F).
The importance of high ENR becomes obvious when the
noise is amplified, because the noise contributions of the
amplifier may be disregarded when the ENR is 17dB larger
than the noise figure of the amplifier (the difference in total
noise power is then less than 0.1dB). The ENR can easily
be converted to noise spectral density in dBm/Hz or μV/√Hz
by use of the white noise conversion formulas in Table 1.
Table 1. Useful White Noise Conversion
dBm
dBm
dBm
dBm/Hz
dBm/Hz
=
=
=
=
=
dBm/Hz + 10log (BW)
20log (Vn) – 10log(R) + 30dB
20log(Vn) + 13dB for R = 50Ω
20log(μVn√Hz) – 10log(R) – 90dB
–174dBm/Hz + ENR for ENR > 17dB
When amplifying noise it is important to remember that
the noise voltage has a Gaussian distribution. The peak
voltages of noise are therefore much larger than the average
or RMS voltage. The ratio of peak voltage to RMS voltage
is called crest factor, and a good crest factor for Gaussian
noise is between 5:1 and 10:1 (14 to 20dB). An amplifier’s
1dB gain-compression point should therefore be typically
20dB larger than the desired average noise-output power
to avoid clipping of the noise.
For more information about noise diodes, please contact
NOISE COM, INC. at (201) 261-8797.
Additional Reading
1. Johnson, J.B, “Thermal Agitation of Electricity in
Conductors,” Physical Review, July 1928, pp. 97-109.
2. Nyquist, H. “Thermal Agitation of Electric Charge in
Conductors,” Physical Review, July 1928, pp. 110-113.
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Information furnished by Linear Technology Corporation is believed to be accurate and reliable.
However, no responsibility is assumed for its use. Linear Technology Corporation makes no representation that the interconnection of its circuits as described herein will not infringe on existing patent rights.
AN61-39
Application Note 61
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AN61-40
Linear Technology Corporation
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