### Capacitor Self-Resonance

```Experiment No. 1.
Telephone Systems and Dialing Tones
By:
Prof. Gabriel M. Rebeiz
The University of Michigan
EECS Dept.
Ann Arbor, Michigan
The circuit diagram of a telephone circuit is shown in Fig. 1. The telephone is generally
connected to the central office using a pair of twisted wires. However, new installations are
using a coaxial-fiber system for wide bandwidth communications. Unlike audio systems with
bandwidths of 20 Hz – 20 kHz for high fidelity sound, a telephone operates over the 300 Hz –
3.3 kHz bandwidth. The reason is that most of the energy of human voice is within this
frequency bandwidth and a 3 kHz bandwidth is enough for reliable conversation (Reliable: yes,
but not excellent!). The bandwidth limitation is the main reason why we have trouble
distinguishing “b” from “p” from “d” over a telephone. The audio voltage swing is 5-500 mV
peak, leading to a dynamic range of 40 dB, which is much lower than hi-fi system (dynamic
range of 70-90 dB).
The telephone operates on a 48 V DC system supplied over a pair of lines from the central
telephone office. This is historical since the telephone was invented before the AC 60 Hz
power distribution system and could not be changed anymore. To grab your attention, the
control office sends bursts of a 20 Hz sinusoidal signal with a 75 V rms voltage to activate the
ringer. The bursts are on for 2 sec and off for 4 seconds. When a party answers the phone,
the telephone switch closes, the central office detects a DC current in the circuit and stops the
ringing signal. You could ask why 75 V? It is huge! The answer is that this signal was needed
to activate inefficient ringers on old telephones. In newer phones with electronic ringers, a TTL
(5 V) digital signal is enough to activate the ringer. However, this telephone system will not be
compatible with old phones!
Twisted Wires
Central
Office
48 V DC
(Voice)
300 Hz
to
3.3 kHz
75 Vrms
20 Hz
Ringer
2s
4s
Blocking
Capacitor
Telephone
Handset
Switch
Ringer
Fig. 1. The home telephone system.
1
Central
Office
The lines between the central telephone office and your home therefore carry:
DC (O Hz) at 48 V:
Powering the phone
20 Hz Bursts at 75 Vrms:
For activating the ringer
300-3,300 Hz at 5 mV – 0.5 V: Voice signal
In order to dial a phone number, you need to transmit specific frequencies which are within the
300 Hz – 3,300 Hz range. However, if you assign a simple frequency to each number, then
somebody whistling when you are dialing (or a large clean sound) can actually cause you to
misdial! A very nice way to solve this interference problem is to send two frequencies for each
number. The probability that two specific frequencies with a ratio equal to a rational number
are present in the background noise when you are dialing is really very low!
The dial pad of a telephone is shown in Fig. 2. When a button is pushed, the two tones
corresponding to the intersection of the vertical and horizontal axes are sent. Notice that no
frequency is the harmonic of any other frequency thereby avoiding problems due to distortion
and harmonic generation (see Lab. 2.2). Also, no frequency can be synthesized from the sum
or difference of any two frequencies, thereby avoiding misdialing problems due to
intermodulation products (see Lab. 3.2).
697
1
2
3
770
4
5
6
852
7
8
9
941
*
0
#
1209
1336
1477
Not
Yet
Used
1633
Fig. 2: A telephone dial-pad. (All frequencies are in Hz.)
2
Experiment No. 1.
Time & Frequency Domain Measurements,
Telephone Systems & Dialing Tones
Goal: The goal of Experiment #1 is to learn how to use the equipment in the lab, and to
measure the output frequencies of a telephone dialer.
Read this Experiment and answer the pre-lab questions before you come to the
lab.
1.0 Time Domain Measurements (or Learning the Agilent
Oscilloscope):
Equipment: Agilent 33120A Waveform Generator
(Replacement model: Agilent 33220A Function / Arbitrary Waveform
Generator)
Agilent 54645A Oscilloscope
(Replacement model: Agilent DSO5012A 5000 Series Oscilloscope)
1. Connect the output of the Agilent 33120A waveform generator to Channel 1 of the
Agilent scope using a coaxial cable.
2. Set the waveform generator to deliver a sinewave at 1 KHz and 2 Vppk. Also, set
the offset voltage to be zero (see p. 4).
Setup
Autoscale
, Default Setup sequence. (Do NOT use the
key. This key
3. Run the
resets a large portion of the scope settings and displays the waveform. By using
this keey you can develop a very bad habit and never learn how to use a scope
well!)
4. Turn the VERTICAL Volts/Div knob of Channel 1 and see how you can expand or
compress the waveform depending on your selection. You will find that you can
easily “saturate” a scope and you should never do this. The waveform must
always be within the display area.
Turn the Position knob to see how you can move the center of the waveform up
and down. Now, center the waveform and choose a 500 mV/div setting.
5. Turn the HORIZONTAL Time/Div knob and see how you can expand or compress
the waveform depending on your timebase selection. If you choose a 200 µs/div
setting, the 1 KHz (/msec period) sinewave “looks” expanded. If you choose a 2
msec/div setting, the 1 KHz sinewave “looks” compressed. Choose a 500 µs/div
setting.
Turn the Delay knob to the right to see how you can delay the triggering time.
Look at the dark small arrows (on top and bottom of the screen). These define the
actual trigger point. Return the delay back to 0.00 s (align the arrows).
6. Trigger Selection: The scope needs a signal to trigger its sampling circuitry. The
triggering signal could be derived from the signal itself or from external or internal
references.
Source
3
key under the TRIGGER section. You will find on the bottom
a. Press the
of the screen:
Ch.1 Ch. 2 External Line
Press Ch. 2: Since you have no input to Channel 2, you will loose your lock
and the signal will not be stable on the screen.
Press Line: The scope is now triggering on the 60 Hz AC line voltage. Since it
is not locked to the 1 KHz waveform, the signal will not be stable on the
screen.
Press External: The scope triggers on an external signal provided by the
external trigger input. Since you have no input, the signal will not be stable on
the screen. You can connect the SYNC output of the Agilent 33120A
waveform generator to the External Trigger input. Your signal will then be
stable on the screen. Do it if you wish.
Press Ch. 1: The scope is triggering back on the input signal and the signal is
stable on the screen. (Remove the external trigger if you have connected it.)
7. Slope/Glitch Triggering: A scope can trigger on the rising edge or falling edge of a
waveform. Look at the left side of the screen. You will find two small dark arrows,
on top and bottom of the screen. These arrows define the triggering plane.
Slope
Glitch
key and choose the rising edge key (see the screen). Look at
a. Press the
the waveform at the “arrow” reference plane. Note that you are triggering at
the rising slope of the sinewave.
b. Choose the falling edge and note that you are triggering at the falling edge of
the sinewave.
c. Return to rising edge trigger mode (we do not use TV or Glitch triggering).
8. Mode/Coupling Triggering: A scope needs a certain voltage level to trigger.
Normally, this is set automatically, but in certain cases, you want to control this
level so that you do not trigger on low level signals or noise.
Mode
Coupling
9.
key and look at the bottom of the screen. The Auto Level is
a. Press the
highlighted.
b. Press the Auto option on the screen, and turn the Level knob under the
TRIGGER section. Look at the waveform. As the triggering level is raised (or
lowered), the scope triggers a bit late (or earlier) so as to align the set level
with the triggering reference plane. When the level is above the waveform
peak, the scope does not trigger anymore and you loose lock.
c. Press the Normal option on the screen and repeat. When the level is above
the waveform peak, you loose the trigger and the waveform freezes. The
scope is not running anymore.
d. Press back the Auto Level option.
e. The Coupling key, AC or DC, means that the signal is either AC or DC
coupled. If it is AC coupled, then the scope will not show the DC level of the
signal.
f. The Reject key introduces low-pass filter with a corner freq. of 50 KHz to
reject all noise above 50 KHz, or a high-pass filter with a corner freq of 50
KHz to reject all noise below 50 KHz. We rarely use this key.
Voltage Measurements: Look at the top of the scope under the Measure section
Voltage
and press the
key. Now look at the bottom of the screen.
a. Make sure that you are on Source 1 (for Channel 1).
b.
Press Vpp, Vavg, and Vrms and write these values in your notebook.
c. Press Clear Meas and then Next Menu.
d. Press Vmax, Vmin, Vtop, Vbase. Do not write them in your notebook.
Time
4
10.
Time Measurements: Press now the
key and look at the bottom of the
screen.
a. Make sure that you are on Source 1 (for Channel 1 signals).
b.
Press Freq, Period, Duty and write these values on your notebook.
c. Press Clear Meas and then Next Menu.
d. Press +Width (positive part of waveform), –Width, Risetime (defined at 10% to
90% of the waveform).
11.
Cursor Measurements: Press the
key and look at the bottom of the screen.
a. You have two cursors, V1 and V2 and you can read any voltage on these
cursors. Also, you can read the difference between V1 and V2 (∆V). Read
Vpeak and Vppk using the cursors.
b. Same for time measurements with t1, t2 and ∆t.
Note that if you want to read the Degrees (or phase of a signal), you need to
calibrate first. Put a cursor at a zero crossing (t1) and put the other cursor one
Cursors
period away ∆t = 1 ms). Press the Deg key and the Set 360˚ key. You have
now calibrated the phase.
2.0 Square-Wave Risetime Measurement:
1. Connect now the Agilent 33120A waveform generator directly to the scope. Set
the Agilent 33120A to give a 10 KHz square-wave with Vppk =2 V.
On the Scope, choose a 500 mV/div setting for Vertical, and a 20.0 µs/div for
Horizontal.
Time
key, then go to the Next Menu and
Go to the Measure section, press the
press the Risetime key. Write your measurements in on your lab notebook.
3. Choose now a 50 ns/div timebase. Notice how the waveform is still triggered
underneath the arrows and you only see the rising edge of the square wave. Draw
the waveform in your lab notebook. (You will see some oscillations called “ringing”
and you will study this in EECS 211.)
4.
Measure the risetime and write it in your lab notebook.
2.
5
3.0 Frequency Domain Measurements:
1. Set the Agilent 33120A to give a 10 KHz sinewave with Vppk = 2V. Connect it to
Channel 1 of the scope.
2. Choose the vertical settings at 0.5 V/div and a horizontal setting (timebase) at
500 µs/div. You will see a lot of sinewaves on the screen.
Entering Math Mode:
+
button.
3. Press the Math Mode
4. At the bottom of the screen, you will see Function 1 and Function 2.
Function 1 does addition (+), subtraction (–) or multiplication (*) on signals of
Channels 1 & 2.
Function 2 does integration (∫dt), differentiation (dv/dt) or a Fast Fourier Transform
(FFT) on signals of Channels 1 or 2, or of the resulting waveform of Function 1
(F1).
5. Press Function 2: ON and Menu
Operand: 1, 2, F1 (Choose the operand to be Channel 1)
Operation: FFT, ∫dt, dv/dt (Choose FFT).
Units/div
10 dB
(Sets the units in dB for the vertical lines)
Ref Level
0.00 dBV
(Sets the top horizontal line in dBV)
6. Press FFT Menu, you will see at the bottom of the screen:
48.8 KHz
(Shows the center freq. Controlled
Center Freq
timebase (horizontal) settings)
by
Freq Scan
97.66 KHz
(Shows the freq. scan. Controlled
timebase (horizontal) settings).
Window
Hanning
(Can be selected between Hanning, flat-top,
Exponential and Rectangular. Always choose
Hanning.)
Autoscale FFT
7. Press Channel 1 button
(Moves 0 Hz to left and autoscales the
vertical settings. I do not like it.)
1
twice to get rid of the time domain representation.
(To view Channel 1 in the time domain, press
time.)
8. Press Math Mode button
screen.
by
+
1
at any
to get back into the FFT menu at the bottom of the
You have in front of you a clear representation of a sinewave signal in frequency
domain. Notice the single peak at 10 KHz (the rest is sampling noise).
9.
10a.
6
Cursors
Press
. Using V1, V2 and f1, f2, measure the amplitude of the sinewave
(in dBV) at 10 KHz and the average amplitude of the noise. Write them in your
lab notebook.
Change the amplitude of the sinewave to 100 mVppk and using the Cursors
mode, measure the voltage in dBV. Write it down on your notebook.
Return the amplitude back to 2 Vppk.
10b.
Using the knob on the function generator, vary the frequency in 1 KHz steps
to 100 KHz and see the peak moving on the screen. Notice what happens
above 100 KHz. The signal returns to the screen and moves backward!! This
is not correct and is due to the sampling circuitry/firmwave of the scope.
THEREFORE, ALWAYS BE SURE THAT YOUR FREQUENCY SPAN (AT
THE TOP OF THE SCREEN) is LARGER THAN YOUR SIGNAL!
Return the sinewave frequency to 10 KHz.
11.
Now comes the interesting part: Press the Square-Wave button (10 KHz,
Vppk = 2V) and measure the frequency and amplitude of the fundamental (fo)
and of each harmonic (3fo, 5fo, 7fo and 9fo). Write them in your lab notebook
in a table form.
12. Press back the sinewave button. Now play with the timebase settings and see
how you change the center frequency and frequency span of the display. Always
choose a setting which puts your fundamental and harmonic frequencies within
the set frequency span!
7
To view Channel 1 in the time domain, press
time.
1
To view Channel 1 in the frequency domain, press
any time.
at any
+
at
The dB Scale: In time domain, the unit is volts or “V.” You can have Vppk, Vrms
or Vav. In frequency domain, the only unit is dB since the rms voltage is needed to
calculate the power carried by a signal. The conversion is quite easy if you have a
calculator.
dB = 20 log (Voltagerms (V))
V rms =
V pk
2
=
V ppk
2
2
Voltage(rms) (V)
dB
Voltage(rms) (V)
dB
10
20
1.0
0
1
0
0.8
–2
0.1
–20
0.5
–6
0.001
–40
0.4
–8
0.001
–60
0.2
–14
0.1
–20
and
(1 mV)
4.0 Telephone Dialing Tones:
Equipment: Agilent 34401A Multimeter
Agilent E3631A Triple Power Supply
Agilent 54645A Digital Sampling Scope
(Replacement model: Agilent DSO5012A 5000 Series Oscilloscope)
Telephone Tone Dialer Mounted on a Circuit Board
Experiment Set-Up:
1. Connect the Agilent 33120A signal generator to the digital scope and measure a 1
Vppk sinewave at 1500 Hz, and a 1 Vppk sawtooth wave at 1500 Hz in time and
frequency domain. (Do not take any data. This is just to get back in the groove!)
2. Set the Agilent E3631A power supply at 4 V. Set the current limit to 100 mA (see
p. 7). Make sure that the (–) terminal of the Agilent E3631A power supply is
connected to the ground ( ) terminal of the circuit board, and the (+) terminal of
8
Agilent E3631A is connected to (+) of the circuit board. Check the voltage applied
to the telephone dialer unit with the Agilent 34401A multimeter .
3. Dial any number(s) you wish and listen to the generated tones.
4.
Neatly graph in time domain the signal resulting from the number 8. Label few
max. and min. values of the waveform. Choose a time span between 1
ms/divison and 5 ms/division which results in a signal with many peaks and
valleys on the screen and “STOP” the triggering of the scope (top right
section). Go into the cursor mode and try to determine the “period” of this
complex waveform (this is a bit tricky) and the corresponding “frequency” (f =
1/ ∆T).
Sketch the time waveform on your notebook and compare it to your pre-lab
exercise.
Now, “RUN” the oscilloscope again and set the FFT correctly. Go into the
cursor mode and measure the signals at the two frequencies (~852 Hz, ~1336
Hz) and their amplitudes in dBV.
Sketch the frequency spectrum on your notebook (do not include the noise)
and label the axes and put the measured values on the graph.
5. Repeat above exercise with any other number of your choose (but not on the
same column or row as #8) and the “*” key.
Sketch the time waveform and frequency spectrum of each signal on your
notebook. Measure and label the frequencies and amplitues corresponding to
each signal.
6. You are now free to play for 5-10 minutes with the dialer but you are not required
to take any data. See how the frequencies jump around but are understandable.
See how different the time waveforms are from number to number, and that we
cannot quickly get a lot of information from them. This is yet another indication
that WE THINK IN FREQUENCY DOMAIN!
9
10
Experiment No. 1.
Time & Frequency Domain Measurements,
Telephone Systems & Dialing Tones
Pre-Lab Assignment
1.
2.
3.
4.
Translate the following dBV numbers into rms and ppk voltages:
+10 dBV
=
________ V
+38 dBV
=
________ V
–10 dBV
=
________ V
–38 dBV
=
________ V
–20 dBV
=
________ V
–60 dBV
=
________ V
+20 dBV
=
________ V
+60 dBV
=
________ V
Translate the following rms voltages into dBV (20 log (Vrms)).
100 V
=
________ dBV
10 mV
=
________ dBV
10 V
=
________ dBV
60 mV
=
________ dBV
1V
=
________ dBV
6 mV
=
________ dBV
100 mV
=
________ dBV
60 µV
=
________ dBV
Translate the following ppk voltages into dBV.
10 V
=
________ dBV
150 mV
=
________ dBV
2V
=
________ dBV
100 mV
=
________ dBV
0.5 V
=
________ dBV
22 mV
=
________ dBV
200 mV
=
________ dBV
3 mV
=
________ dBV
What is the meaning of a signal period (T)?
What is the period and frequency of a DC signal?
What is the period of a 10 kHz signal in msec?
5.
Derive the Fourier-Series expansion of a square-wave. Calculate the Fourier
coefficients of a 10 KHz (fo), 2 Vppk square wave up to 13 fo. The DC level of the
square-wave is zero.
Write your answers in Volts (rms) and dBV for the fundamental and each harmonic
frequency in a table form. You will need this table for comparison with experimental data.
11
V
+1V
t
–1V
100 µs
6.
Take two sinusoidal signals at 852 Hz and 1336 Hz (number 8).
v1 (t) = cos (2π (852) t)
v2 (t) = cos (2π (1336) t)
Plot: v (t) = v1 (t) + v2 (t) Use MATLAB (attach your computer code with your plot and
remember to include your name and date of work in the title of your plot).
x-axis = 0 - 0.01 sec. (choose small time steps)
y-axis = –2 to + 2 V
The resulting waveform is complex. Look carefully at the graph: Can you find the
period, T, of the complex waveform? What are the max. and min. voltages? Write
7.
12
If a circuit exhibits non-linear behaviour, it will generate harmonics and intermodulation
products between two signals. For f1 = 852 Hz and f2 = 1336 Hz (number 8), calculate
the following harmonic and intermodulation frequencies:
2f1, 2f2, f2 – f1, f2 + f1, 2f2 – f1, 2f2 + f1, 2f1 – f2, 2f1 + f2.
The (2f1), (3f1), ... and (2f2), (3f2), ... are called the harmonics of the signals.
The (f1 - f2), (f1 + f2), (2f1 + f2), ... are called the intermodulation products of the
signals.
Do not be surprised if you find some of these frequencies on your dial-tone spectrum.
Experiment No. 1.
Time & Frequency Domain Measurements,
Telephone Systems & Dialing Tones
Lab Report Assignment
1. Compare the measured dBV values of the 10 KHz square-wave (fundamental and
harmonics) with the calculated values in your pre-lab. Organize the data in a table format
and show difference in dB.
2.
Take the measured spectrum of the 10 kHz square-waveform at fo, 3fo, 5fo, 7fo, 9fo
and plot the following waveforms from t=0 to t=0.3 msec. Note that Vfo, V3fo, ... are
rms values!
v 1 ( t) = 2 V(f ) sin (2 π f o t )
o
v 2 (t) = v 1 (t ) +
v 3 (t ) = v 2 (t ) +
[
2 [V
(fundamental)
V in rms!
]
2 V(3f o ) sin (2 π (3f o ) t) + V(5f o ) sin (2 π (5f o )t)
(7f o )
]
sin (2 π (7f o )t )+ V(9f ) sin (2 π (9f o )t )
o
(Up to the 5th harmonic)
(Up to the 9th harmonic)
Do these summations using MATLAB. The 3 plots should be well detailed with an x
axis in msec (0–0.3 msec) and a y-axis in volts (+2 V). Your time steps should be
small enough to clearly see the waveforms.
Reminder: Do not forget to attach your MATLAB code with every plot, and include
your name and date of work in the title of each plot.
The essential point behind this exercise is to clearly “see” how any periodic waveform
(square wave or other) is actually composed of a fundamental component (fo) and a
series of higher frequencies called harmonics. In the case of a square wave, you need
at least up to 5fo before it starts looking like a square wave and up to 9fo before it
becomes a good square wave. This means that a 100 MHz square-wave clock
computer must be designed so that the computer lines (on-chip and off-chip) pass at
least up to 500 MHz sinusoidal signals for proper operation. DO NOT FORGET THIS!
3. a) Translate the meaured dBV of the spectrum of #8 into Vrms and plot the following
function using MATLAB.
(
)
V1 (t ) = 2 Vrms (f ) cos (2 π (f1 )t )+ Vrms (f ) cos (2 π (f2 )t )
1
2
where f1 and f2 are
your
measured
frequencies for #8.
This is the ideal #8 waveform as per your pre-lab (but with a different vertical
scale).
b) One frequently asked question is the use of cos (2 π ft) or sin (2 π ft) functions. You
will learn later in the course that there is a difference between them, and it is called
“phase shift.”
To see the difference, plot V2(t) and V3(t) on the same graph using MATLAB.
V2 (t) = cos (2 π f1 t) + cos (2 π f2 t)
V3 ( t) = cos (2 π f1 t) + sin (2 π f2 t)
x − axis = 0 − 0.004sec
y − axis = − 2 to + 2 V
13
f1 = 852 Hz f2 = 1336Hz
Write a brief statement on the comparison between V2(t) and V3(t).
These experiments have been submitted by third parties and Agilent has not tested any of the experiments. You will undertake any of
the experiments solely at your own risk. Agilent is providing these experiments solely as an informational facility and without review.
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OF ANY OF THE EXPERIMENTS.
14
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