ETC AB-185

APPLICATION BULLETIN
®
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AUTOMATIC GAIN CONTROL (AGC)
USING THE DIAMOND TRANSISTOR OPA660
By Christian Henn, Burr-Brown International GmbH
Multiplication of analog signals has long been one of the
most important nonlinear functions of analog circuit technology. Many signal sources, however, such as CCD sensors, pin diodes, or antennas, deliver weak, oscillating, and
simultaneously wide-band signals. But now a new multiplication method is available. Used as a wide-bandwidth Automatic Gain Control (AGC) application circuit, the integrated
circuit OPA660 varies its own gain to change the signal
amplitude and keep the output signal constant over a wide
input voltage range. The OPA660 thus makes it possible to
control and amplify signals with no additional multiplier.
Important parameters include the differential gain (DG), the
thermally induced pulse distortion, and the signal-to-noise
ratio (S/N).
An analog multiplier delivers an output signal (voltage or
current) that is proportional to the product of two or more
inputs. The application circuit presented here is concerned
primarily with two inputs. In the simplest case, each of the
two inputs can function with both polarities. In this case, the
input voltage swing covers all four quadrants; that is, there
are four polarity combinations. In contrast to a four quadrant
multiplier, a two quadrant multiplier allows only one input
to be connected to a signal of any polarity. The second input
can only process unipolar signals.
quiescent current programmer, it can also be used for multiplicative applications.
Figure 1 illustrates the dependance of the transconductance
(gm = d(IOUT)/d(VIN)) upon the resistance, RQC. The following equation can be derived from the idealized OPA660
model circuits shown in Figure 2.
V
IQC = T ln (n)
RQC
When the temperature voltage (VT) is 25.86mV, the quiescent current resistance (RQC) is 250Ω, and the scale factor (n)
of the transistor R122 is 10, the cross current IQC can be
calculated as follows:
IQC =
25.86mV
ln(10) = 238µA
250Ω
The quiescent current of the subsequent transistor stages can
be calculated with a scale factor (a) of 7.3 for transistors 31,
32, 81, and 82 to
IQC' = a • IQC = 7.3 • 238µA = 1.74mA
IOUT (mA)
Multipliers are nonlinear and thus can not be implemented
as simply and exactly as linear components. In developing
the circuit, various design methods were used depending
upon the accuracy, bandwidth, and justifiable complexity.
Multipliers do have several disadvantages, including linearity errors, temperature dependence, less than ideal crosstalk,
and limited bandwidth, but the multiplication function presented here functions directly and has variable
transconductance, enabling it to achieve the largest possible
bandwidth.
RQC
1.5
250
1.0
500
0.5
–20
–15
–10
10
15
20
VIN (mV)
–0.5
–1.0
AGC WITH THE DIAMOND TRANSISTOR
The voltage-controlled current source of the OPA660 from
Burr-Brown has acquired various nicknames according to its
applications:
–1.5
VOUT = VIN
Operational Transconductance Amplifier (OTA)
Current Conveyor
Diamond Transistor
Ideal Transistor
Macrotransistor
VIN
1993 Burr-Brown Corporation
VOUT
RQC
Applications for the OPA660 are usually amplifier
circuits. But although the OPA660’s connection pin,
IQ, adjusts functions primarily as a power supply switch or
©
M
M
RQC
FIGURE 1. Schematic Diagram of the Multiplication
Function.
AB-185
Printed in U.S.A. October, 1993
BC
7
(13)
DB
7
(13)
DT
7
(13)
IQC'
7.3(x)
IQC'
IQC
81
IQC
IQC
Rgm
IQC
31
8
6
5
IQC'
7.3(x)
2
3
7.3(x)
32
82
10(x)
(14)
122
IQC'
IQC
(14)
IQC'
IQC
7.3(x)
(14)
IQC'
4
4
4
RQC
250Ω
FIGURE 2. Idealized Model Circuit.
Now it is easy to determine the transconductance using the
following equation:
gm =
IQC
VT
=
gm, since it is dependent upon the modulation. This change
results in turn in signal distortion. The following equations
derive the relation between the signal amplitude and distortion.
a • ln(n)
= 67mA/V
RQC
VOUT = i • ROUT = VIN • gm • ROUT = VIN •
i = I1 – I2 = IQC' Exp +
M
RQC
ϕ=
VIN – Rgm • i
VIN + 2IQC' Rgm • sinh (ϕ)
∆V
=
=
2VT
2VT
VT
VIN = 2VT • ϕ –2IQC' Rgm • sinh (ϕ)
a • ln(n) • ROUT
d(i)
= –2IQC' • cosh (ϕ)
d(ϕ)
RQC
= ±10mV
7.3 • ln(10) • 2.08kΩ
250Ω
∆V
VT
( )
– Exp –
i = –IQC' [Exp (–ϕ) – Exp (+ϕ)] = –2IQC' • sinh (ϕ)
When the resistor (ROUT) has 2.08kΩ and the input voltage
is ±10mV, the output voltage reaches the following value:
VOUT =
∆V
VT
( )
The circuit diagram of the actual multiplier circuit as illustrated in Figure 3 makes it easier to determine the multiplication constant, M. The signal current at Pin 8 produces the
following output voltage at the resistor ROUT:
= ±1.4V
d(VIN)
d(ϕ)
= –2VT –2IQC' Rgm • cosh (ϕ)
The multiplication constant M can be derived directly from
the equation as follows:
cosh (ϕ) = sinh2 (ϕ) + 1 =
M = a • ln(n) • ROUT = 7.3 • ln(10) • 2.08kΩ = 35kΩ
( )
i/IQC'
2
2
+1
The gain G can be calculated using the equation:
G=
d(VOUT)
d(VIN)
=
M
35kΩ
=
= 140
RQC 250Ω
gm =
DETERMINING THE
DIFFERENTIAL GAIN (DG)
d(i)
d(VIN)
=
VT
Rgm +
IQC'
2
d(VIN)/d(ϕ)
( )
i/IQC'
2
1
=
1
=
Figure 4 shows the circuit part important for the multiplication. When VIN = 0, i = 0, and I1 = I2 = IQC’, i increases with
rising VIN, resulting in variation of the currents I1 and I2. The
increase in both currents also changes the transconductance
d(i)/d(ϕ)
2
+1
Rgm –
VT
IQC' cosh (ϕ)
IQC' =
gm0 =
DG =
gmMAX
The following applies for low modulation:
a • ln(n) •VT
iMAX ≈
RQC
1
or for low modulation:
–1=
VT/IQC'
Rgm +
(
2
+1
a • ln(n) Rgm/ (RQC + 1)
a ln(n) Rgm/RQC +
VIN/VT
2 (a • ln(n) Rgm/ (RQC + 1)
2
+1
8
5
VIN
±10mVp0
–1
1
VOUT
±1.4Vp0
i
+1
2 (Rgm +VT/IQC')
ROUT
2.08kΩ
7
2
VIN/IQC'
2
≈
+5V
VT/IQC'
Rgm +
)
iMAX/IQC'
Rgm + VT/IQC'
DG ≈
Rgm + VT/IQC'
gm0
Rgm + VT/IQC'
In the extreme case in which Rgm = 0, the following results:
i=0
Rgm + VT/IQC'
VINMAX
3
DB OPA660 DT
4
6
Rgm
1mΩ
2
DG0 =
(
iMAX/IQC'
DG0 ≈
(
VINMAX
2
)
+1 – 1
)
+1 – 1
1
RQC
250Ω
2VT
2
Figures 5 through 8 show an analysis of the equation
DG = f (VIN; Rgm; RQC), which determines the differential
gain error dependent upon the input voltage. The figures
include the open-loop gain resistance (Rgm) and quiescent
current resistance (RQC).
–5V
FIGURE 3. Multiplier Circuit.
As is evident, Rgm produces transfer linearization, but it also
reduces the gain, GRgm.
IQC'
VIN
IQC'
∆V
I1
i
Rgm
I2
i
I2
GRgm =
d(VOUT)
d(VIN)
∆V
Rgm +
IQC'
ROUT
Rgm +VT/IQC'
ROUT
=
I1
=
RQC
i=0
a • ln(n)
IQC'
As will be shown later, the gain reduction results in a poorer
signal-to-noise ratio (S/N). Designers can determine the best
performance compromise for DG and S/N by choosing
appropriate values for VINMAX and Rgm. However, the larger
the control range —that is, the greater the variation of RQC
—the poorer the quality of the compromise that can be
attained.
FIGURE 4. Multiplier Section.
3
10
0
DG max
RQC = 250Ω
3
0
RQC = 500Ω
10
3
20
1
(%)
Rgm (Ω)
(%)
10
1
30
40
20
0.3
50
0.3
30
Rgm (Ω)
DG max
10
40
0.1
0.1
–20
–10
0
10
–20
20
–10
10
0
VIN (mVpo)
FIGURE 5. Differential Gain Error (RQC = 250Ω).
FIGURE 6. Differential Gain Error (RQC = 500Ω).
10
10
3
20
1
30
40
50
(%)
RQC = 1kΩ
0.3
0
10
20
30
40
50
RQC = 2kΩ
3
Rgm (Ω)
DG max
0
Rgm (Ω)
DG max
10
(%)
20
VIN (mVpo)
1
0.3
0.1
0.1
–20
–10
0
10
20
–20
–10
10
0
VIN (mVpo)
20
VIN (mVpo)
FIGURE 8. Differential Gain Error (RQC = 2kΩ).
FIGURE 7. Differential Gain Error (RQC = 1kΩ).
When Rgm is inserted, the relation between the gain, GRgm,
and the control value, 1/RQC, becomes disproportionate.
Reference for VOUT
–
+
AUTOMATIC GAIN CONTROL (AGC)
Circuit tolerances and insufficient temperature compensation result in undefined gains (GRgm = f(RQC)) of about ±25%.
If RQC is implemented by a FET, this undefined gain range
increases even more. These problems can be avoided by
using an AGC circuit as shown in Figure 9.
Automatic Gain Control
VIN
VOUT
Multiplier
Amplifier
Level Control
In the detailed circuit in Figure 10, the ±0.7V input signal
(VIN), which is assumed for now as a constant, is divided by
the input divider (4kΩ/56Ω) to about ±10mV. The 4kΩ
resistor in front of the circuit can, of course, be removed if
the input amplitude is only in the mV range, as is the case
in fiber optic transmission receivers. The amplifier (OPA621)
placed after the circuit converts the output current i of the
multiplier (OPA660) into voltage. The peak detector and
comparator compare the ±1.4V output signal (VOUT) with the
given reference value +1.4V and connect the control voltage
to the FET. This control ensures that the peak value of VOUT
is identical to the adjustable reference DC voltage and is
FIGURE 9. AGC Circuit (Schematic).
unaffected by circuit tolerances. It is also possible to control
the output voltage against the black level or synchronization
level by acquiring the output voltage for comparison only
during the horizontal sync time. While the luminance signal
changes over time, the sync level is always transmitted with
constant amplitude. Such regulation enables the video signal
to be transmitted at a constant amplitude despite changes in
the luminance signal.
4
VOUT
±1.4Vp-p
+5V
3
2
7
OPA621
6
4
ROUT
2.08kΩ
–5V
+5V
i
±10mVp-p
8
7
+5V
OPA660
4kΩ
VIN
5
DB
10kΩ
22kΩ
3
DT
56Ω
Offset
–5V
56Ω
6
4
±0.7Vp-p
–5V
Rgm
1mΩ
2
1
RQC
250Ω
Peak Detector
and Comparator
1.4V
+5V
–5V
–5V
Reference for VOUT
FIGURE 10. AGC Amplifier for Various Signals.
+5V
To Multiplier
Pin 1
+5V
100kΩ
2.7kΩ
0.47µF
+1.6V
Reference
for
VOUT +0.4V
0.47µF
100Ω
100Ω
1kΩ
330Ω
2811
RQC
2*
BC577
2N5460
2.2MΩ
VOUT
±1.4Vp-p
2811
2.2MΩ
+
0.47µF
1MΩ
–5V
FIGURE 11. Peak Level.
To Multiplier
Pin 1
+5V
Variations in the input signal amplitude cause the control
system to produce constant output signal amplitudes
corresponding to the reference value. Simultaneous changes
in VIN and the reference value are also possible.
VOUT
3
7
CA3080
6
∞
2
5
4
10kΩ
DETERMINING THE MAXIMUM DIFFERENTIAL
GAIN (DGMAX) OF AGC AMPLIFIERS
–5V
Hk
47kΩ 0.1µF
2N3904
The input voltage of AGC amplifiers varies from VINMIN to
VINMAX. To maintain a constant output voltage (VOUT) over
this range, the control voltage from the peak level control
varies the resistance RQC correspondingly from RQCMIN to
R QCMAX. The largest signal distortions measured as
4Vp-p
1N4148
–5V
FIGURE 12. Clamp Circuit for TV Signals.
5
C hold
1µF
differential gain (DGMAX) happen at VINMAX or RQCMAX, thus
during operation of the OPA660 with the smallest quiescent
current IQ. For the control range q of the AGC amplifier, the
following conditions apply:
q=
It should be kept in mind, however, that this equation is
based upon the simplified model shown in Figure 2 and
sometimes deviates from measurements and simulation results. The measurements, for example, also include distortion from the subsequent amplifier OPA621. Figures 13 to
15 give an overview of the achievable distortion. For maximum input voltages (VINMAX) from ±10mV to ±20mV and
open-loop resistances from 0Ω to 50Ω, the differential gain
shown in simulations is a function of the ratio VINMAX/VINMIN
and equals 9. Figure 16 presents measured achievable distortions in the AGC structure, as already shown in Figure 10.
VINMAX
VINMIN
RQCMAX = q • RQCMIN + a • ln(n) • Rgm • (q – 1)
B = a • ln(n) • Rgm/RQCMAX
THERMALLY INDUCED DISTORTION
As shown in Figure 2, the power consumption of transistors
31, 32, 81, and 82 varies according to the signal curve. This
variation leads to temperature oscillation and finally to
change in the transconductance gm.
From these equations, it is possible to derive the maximum
distortion, DGMAX, as a function of B and the maximum
input voltage.
At first glance, it looks as if the pulse distortion is caused by
RC parts. The visible thermal time constant, however, is in
the microsecond range and is negatively affected by unequal
temperature distribution on the chip.
B+1
DGMAX =
1
B+
2
VINMAX/VT
+1
2 (B + 1)
As Figure 17 shows, Rgm can reduce this thermally induced
pulse distortion.
10
DGMAX
DGMAX
VINMAX = 10mVp0
1.0
(%)
0
10
20
30
40
50
0.3
1.0
0.3
VINMAX/VINMIN
VINMAX/VINMIN
0.1
0.1
1
2
3
4
5
6 7 8
1
2
3
4
5
6 7 8
FIGURE 14. DGMAX of the AGC Amplifier (Simulation)
(VINMAX = ±15mV).
FIGURE 13. DGMAX of the AGC Amplifier (Simulation)
(VINMAX = ±10mV).
10
3.0
1.0
DGMAX
VINMAX = 20mVp0
0
10
20
30
40
50
3.0
(%)
VINMAX = 20mVp0
Rgm (Ω)
DGMAX
0
10
20
30
40
50
0.3
1.0
Rgm (Ω)
10
(%)
0
10
20
30
40
50
3.0
Rgm (Ω)
(%)
3.0
VINMAX = 15mVp0
Rgm (Ω)
10
0.3
VINMAX/VINMIN
VINMAX/VINMIN
0.1
0.1
1
2
3
4
5
6 7 8
1
FIGURE 15. DGMAX of the AGC Amplifier (Simulation)
(VINMAX = ±20mV).
2
3
4
5
6 7 8
FIGURE 16. DGMAX of the AGC Amplifier (Measurement)
(VINMAX = ±20mV).
6
In contrast, periodic RF signals less than 1MHz are barely
affected by the pulse distortion. The temperature change can
no longer follow the signal change, resulting in more balanced temperature distribution on the chip.
10
8
VINMAX = 20mVp0
DGMAX
0
6
20
(%)
DEMO BOARD
All available measurements were conducted using the completely dimensioned circuit shown in Figure 19. The demo
board designed for this application contains four circuit
blocks. As a differential amplifier with current output, the
OPA660 allows users to control the transconductance by
varying the total quiescent current. Functioning mainly as a
multiplier, it also enables a shift in DC position of the output
voltage by varying the noninverting OPA660 input. The
OPA621 functions as a current-to-voltage converter and
amplifies the signal. The switch, S1, in the shift block lets
the user choose between manual, and automatic offset compensation, and clamped DC restoration. At active LOW, the
clamp pulse triggers the OTA module CA3080, checks the
output voltage (VOUT) against the reference value for the
black level voltage, and stores the correction voltage up to
the next clamp pulse (HK) in the capacitor CHOLD. The fourth
block is the already mentioned peak level control circuit.
The discrete differential amplifier checks the peak value of
the output voltage (VOUT) against the reference voltage set by
PREF. The transistor 2N5460 changes the quiescent current
according to the difference, thus varying the transconductance
gm.
30
40
50
2
Rgm (Ω)
10
4
VINMAX/VINMIN
1
1
2
3
4
5
6 7 8
FIGURE 17. Effect of Rgm on Thermal Pulse Distortion.
64
VINMAX = 20mVp0
60
52
48
44
VINMAX/VINMIN
40
1
For applications requiring frequencies of more than 80MHz
and a controlled output voltage (VOUT) of more than ±1V, we
recommend two-stage gain using two OPA621s. With the
amplifiers OPA622 and OPA623, it will be possible to
increase the bandwidth even more.
2
3
4
FIGURE 18. S/N of AGC Amplifiers.
7
5
6 7 8
0
10
20
30
40
50
Rgm (Ω)
S/N (dB)
56
+5V
Amplfier
R6
100Ω
10nF
2.2µF
9
OPA621
2
R7
VOUT
20kΩ
4
2.2µF
10nF
0.2 ... 0.8Vp-p
VOUT
2.8Vp-p
7
3
–5V
+5V
Level-Shifting
POFFSET
+5V
2.2µF
i
VIN
DB
10nF
3
DT
7
CA3080
4
R8
10kΩ
+5V
R3
56Ω
OPA660
R1
56Ω
C5
+470µF
3
4 Clamped
8
–
Automatic
S1
5
R4
22kΩ R5
56Ω
±13mV
2
1
10nF
RIN
2kΩ
–5V
Manual
7
6
R2
51Ω
10nF
2
3
CHOLD
C4 R
20
1µF 10Ω
2
5
2.2µF
R11
1kΩ
6
1
Rgm
2.2µF
R22
1kΩ
10nF
2.2µF
–5V
0.1µF
Multiplier
R9
51Ω
R21
47kΩ
R23
560kΩ
–5V
C6
0.1µF
4Vp-p
–5V
+5V
+5V
Peak Level-Control
220µF
PREF
VREF
1kΩ
+0.4V
R17
330Ω
R10
R18
100kΩ
R16
2.7kΩ
+1.6V
D1
HK
2N3904
–5V
–
C2
+ 0.47µF
2811
RQC
R14
2.2MΩ
R13
100Ω
R15
100Ω
– C
3
+ 0.47µF
2*
BC577
2N5460
+
–
C1
4.7µF
D2
2811
R12
2.2MΩ
R19
1MΩ
220µF
–5V
FIGURE 19. Circuit Diagram of the AGC Amplifier Demo Board.
8
FIGURE 20. Layout of the AGC Amplifier Circuit Board — Back.
FIGURE 21. Layout of the AGC Amplifier Circuit Board — Front.
9
PARTS LIST
NUMBER
OF PARTS
NO.
DESIGNATION
PART NAME/VALUE
1
IC1
OPA621KP
1
2
IC2
CA3080
1
3
IC3
OPA660AP
1
4
T1, T2
BC577
2
5
T3
2N5460
1
6
T4
2N3904
1
7
D1 , D2
2N2811
2
8
D3
IN4148
1
9
R1, R3, R5
56Ω
3
10
RIN
2kΩ
1
11
Rgm
51Ω
1
12
R6, R13, R15
100Ω
3
13
R7
20kΩ
1
14
R4
22kΩ
1
15
R8, R20
10kΩ
2
16
R11, R22
1kΩ
2
17
R23
560kΩ
1
47kΩ
1
2
18
R21
19
R10
20
R12, R14
2.2MΩ
21
R18
100kΩ
1
22
R17
330Ω
1
23
R16
2.7kΩ
1
24
R19
1MΩ
1
1
25
Capacitor 2.2µF
6
26
Capacitor 10nF
6
Capacitor 220µF
2
28
27
C2 , C3
Capacitor 0.47µF
2
29
C5
Capacitor 470µF
1
30
C6
Capacitor 0.1µF
1
31
C4
Capacitor 1µF
1
32
PREF POT 1kΩ
1
33
POFFSET POT 10kΩ
1
34
VIN, VOUT, HK SMA
3
35
POS, GND, NEG Mini-Banana
3
10