Formal Report
Attenuator Coaxial-Cable Oscilloscope Interface
ECE 207
Brandon Goldstein
Station 7
March 30, 2012
Attenuator Coaxial-Cable Oscilloscope Interface
Brandon Goldstein
3/30/2012
Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Theory and Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4,5
Methods
Equipment List. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Instructions for Technician. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6, 7, 8
Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
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Attenuator Coaxial-Cable Oscilloscope Interface
Brandon Goldstein
3/30/2012
Abstract
The objective of this study is to build a simple attenuator capable of reducing the
amplitude of a given input without distorting the waveform. A circuit was assembled with a
voltage divider connected to an oscilloscope. The open-ended coaxial cable capacitance must
first be calculated before the two resistors in the voltage divider can be determined. These two
resistors are used to ensure that the oscilloscope is not overloaded, and the appropriate
amount of gain is produced. With an oscilloscope in parallel, one can check to see if the
specifications have been met. It was concluded after building and testing the circuit that the
attenuator design meets all the constraints given.
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Attenuator Coaxial-Cable Oscilloscope Interface
Brandon Goldstein
3/30/2012
Introduction
The objective of this experiment was to correct a method used incorrectly by an
engineer, by making a 0.5 and a 0.8 attenuator. The engineer was trying to make an attenuator
that had a time constant of 250 nanoseconds, a frequency of 100 kilohertz, and 5 volts from
peak to peak. He tried to use a 1 Mega-ohm resistor and put it in the voltage divider.
Unfortunately, this provided a time constant that was too slow, which produced a triangular
wave and therefore didn’t work (the setup he used is shown in figure 3). Using techniques
learned in lab 8, models were applied in order to make an attenuator that met the qualities
needed. The value of capacitance in the open-ended coaxial cable was measured with the
oscilloscope (x10 probe). Using calculations and the setup shown in figure 4 and 2, determine
the necessary resistors needed in order to meet the amplitude and time constant
specifications. Calculations and theory are provided to support the results and explain how the
components work.
Theory and Calculations
An attenuator is an electronic device that reduces the amplitude or power of a signal
without affecting the waveform that is sent through it according to Weber Attenuators (Weber
Attenuators). The first circuit that the engineer made (figure 3) produced a time constant that
was too slow. The cable acts and is modeled as a capacitor in figure 2. The procedure to make
the .5 attenuator is as follows:
1. Measure C_cable
2. Determine R_total
R_total=[R_s+R_ext]||R_c||R_sc
3. Find C_T
C_T=T/R_total
4. Find Capacitance
C=C_T-C_sc
5. Calculate the time constant (T<250 ns) (defines upper limit)
T=RC
6. Determine the upper and lower bounds for R_A and R_B (R_A+R_B)>2000 ohms (defines
lower limit)
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Attenuator Coaxial-Cable Oscilloscope Interface
Brandon Goldstein
3/30/2012
[(R_A+R_S)||R_B||R_SC]*(C_cable+C_sc)<250 nanoseconds
Methods
Equipment List
1.
2.
3.
4.
5.
6.
7.
8.
AGILENT 54621A Oscilloscope
AGILENT 33120A Arbitrary Function Generator
AGILENT 33401A Digital Multimeter
1 MΩ resistor
470 Ω resistor
500 Ω resistor
Cables
Calculator
Procedure
1.
2.
3.
4.
5.
Measure the capacitance of the oscilloscope probe
Calculate R_A and R_B to produce a gain of .5
Construct the circuit in Figure 2 using the values calculated
Measure the gain and time constant of the circuit to verify that they are correct.
Repeat steps 1-3 with an R_A and R_B to produce a gain of .8.
Figure 2
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Attenuator Coaxial-Cable Oscilloscope Interface
Brandon Goldstein
3/30/2012
Figure 4. Wiring Diagram for Improved Design
Instructions for Technician
Measure the capacitance of the x1 probe by using a x10 probe. Next, construct the
circuit as seen in figure 2 and 4. Determine R_A and R_B to meet the amplitude, time constant,
and a gain of 0.8. The oscilloscope needs to have the following constraints: 100 KHz square
wave, 5 volts peak to peak, and a time constant less than 250 nanoseconds. Use the
oscilloscope to determine the actual time constant. Next, calculate the total resistance of the
circuit. Using the time constant and total resistance calculate the capacitance of the cable.
Once you have all these values, you can calculate R_A and R_B. Finally, calculate the percent
error in your procedure.
Results
In our case: Givens: 100Khz square wave
5 volts pk-pk
τ≤ 250 nanoseconds
R_c=∞
R_sc(x10 probe) = 10 MΩ
R_sc(x1 probe) = 1 MΩ
R_s= 50 Ω
C_sc(x10 probe )= 2 pF
C_sc(x1 probe) = 14 pF
1. Determine R_total (assume R_c is negligible)
R_total=[R_s+R_ext]||R_c||R_sc
R_total=10039.9 Ω
2. Determine Time constant (from oscilloscope and plot 1)
τ=2.080µs
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Attenuator Coaxial-Cable Oscilloscope Interface
Brandon Goldstein
3/30/2012
3. Calculate C_cable
C_t= τ/R_total
C_t= 2.09e-10 F
C_cable= C_t-C_sc
C_cable= 2.07e-10 F
4. Calculate R_A and R_B
.5= [R_B||1 M]/ [R_B||1 M + (R_A+50)]
a. Choose arbitrary R_B/R_A value
5. Calculated Time constant
R_B/(R_B+R_A)=.5
R_B= 1500 Ω R_A= 1500 Ω
250 ns > (R_A||R_B)(C_cable+14 pF) = τ
τ= 1.66e-7
6. Calculate percent error
((Measured-actual)/actual) *100 = % error
% error = 11%
7. Repeat steps 4-6 for 0.8 gain attenuator
Calculated values: R_B= 6800 Ω
R_A= 1500 Ω
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τ= 1e-5 s
0% error
Attenuator Coaxial-Cable Oscilloscope Interface
Brandon Goldstein
3/30/2012
In summary, our results that were calculated were very close to the measured values.
Both these values were satisfactory in creating and fixing the original problem that the engineer
had in making a 0.5 attenuator.
Conclusion
The objective of this lab was to build a simple attenuator capable of reducing the
amplitude of a given input without distorting the waveform. To satisfy the objective, a circuit
was designed, built, and tested in order to match the given constraints. From the procedures
above it was determined that our measured and calculated values were acceptable in the fact
that the percent error was relatively small. These values were also suitable for the given
constraints that the engineer was trying to achieve, therefore we solved the problem.
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