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ELEC 350L
Electronics I Laboratory
Fall 2012
Lab #5: Digitally Controlled Attenuator – Part 2
Introduction
Last week in Part 1 of this lab exercise, you designed a circuit to supply a variable voltage using
a binary up/down counter and a multi-input scaling and level-shifting circuit. This week, you will
design and assemble the attenuator circuit that will be controlled by the variable voltage supply.
You will then test the complete attenuator system to verify that it can control the amplitude of a
sinusoidal signal.
Pre-Lab Work and Quiz
Before arriving at the lab session, read over the “Theoretical Background” and “Experimental
Procedure” sections of this handout carefully, and perform the calculations necessary to fill in
the blank spaces in Table 1. At the beginning of the lab session, submit a completed table
accompanied by a brief explanation (with equations) of how you calculated the required data.
The pre-lab work may be handwritten on loose-leaf paper, and it will not be graded for style,
formatting, spelling, and grammar. However, it must be legible and easy to follow.
Theoretical Background
Recall that the i-v characteristic of a pn-junction diode is described by the diode equation,


i D  I S e vD / nVT  1 ,
where, as shown in Figure 1, iD is the current flowing through the diode in the direction of the
arrow in the circuit symbol, and vD is the diode voltage, which obeys the passive sign convention
(i.e., iD flows into the positive side of vD). The constant IS is the reverse saturation current, and
the constant n is the empirically determined emission coefficient, the value of which varies
between one and two for most silicon diodes. The constant VT is the thermal voltage, given by
VT 
kT
T
,

q 11,600
where T is the temperature in kelvins; k is Boltzmann’s constant (1.38 × 1023 J/K); and q is the
charge on a single proton (1.60 × 1019 C). At a temperature of approximately 293 K (20 C or
68 F), VT ≈ 25 mV.
iD
+ vD −
Figure 1. Definitions of diode current and diode voltage. Both quantities are
positive if the diode is forward biased.
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As we have seen, it can be difficult to solve circuit problems using the diode equation because of
its nonlinear form. The piecewise linear (PWL) model of the diode has therefore been developed
to approximate the i-v characteristic. Its circuit representation consists of linear circuit elements,
specifically, an independent voltage source VF in series with a resistor rd. The i-v characteristic
that corresponds to the PWL model is shown as a dashed line in Figure 2, and the actual i-v
characteristic described by the diode equation is shown as a solid curve. The accuracy of the
model depends on evaluating the slope of the curve near the operating point of the diode, the part
of the curve associated with the expected current through (or voltage across) the diode during
normal operation. The reciprocal of the slope is equal to the value of the “on” resistance rd, more
commonly called the diode small-signal resistance or the incremental resistance. If the diode
current fluctuates significantly, it might be pointless to determine the value of rd since it too
would fluctuate. However, in a situation where the current varies only a small amount around an
average value, the inclusion of rd in the diode model can be very helpful. As we shall see, it is
central to the design of diode-based attenuators.
iD
slope = 1/rd
vD
VF
Figure 2. Piecewise linear (PWL) representation of the i-v characteristic of a pnjunction diode. The PWL representation can be modeled as an independent
voltage source of value VF (which represents the diode’s turn-on voltage) in series
with a resistor of value rd.
Many types of attenuator circuits use the internal resistances of one or more diodes as elements
of a voltage divider (or more sophisticated voltage reduction circuits). A simple approach is
illustrated in Figure 3. Resistor RB and control voltage VS are chosen to establish a “quiescent,”
or average, DC current flowing through the diode. The time-varying signal coming from the
function generator (represented by vg and Rg) is assumed to be weak enough so that the current it
causes to flow through the diode is a tiny fraction of the DC current. Thus, the diode’s “on”
resistance rd is not significantly affected by the signal current.
The two capacitors C1 and C2 connected to the anode of the diode in Figure 3 are called DC
blocking capacitors, and their purpose is to keep DC current from flowing anywhere but through
the diode. If they have large enough values, they will pass AC signals easily. Recall that the
reactance of a capacitor can be determined via
XC  
1
.
2 f C
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C3
VS
Function
Generator
Rg
vg
+
−
RB
C1
C2
+
vD
−
iD
+
vo
−
RL
Figure 3. A simple diode-based attenuator. Resistor RB sets the DC component of
the diode current, which in turn controls the diode’s “on” resistance rd. If RL >> rd
and RB >> rd, then the effect of those two resistors can be ignored, and the on
resistance can be assumed to form a voltage divider with the function generator’s
output resistance Rg.
The values of C1 and C2 are chosen so that their reactances are insignificant compared to Rg, rd,
and RL at the lowest frequency of interest (where XC is greatest in magnitude). The capacitor C3
in parallel with the power supply VS ensures that any signal current that flows through resistor RB
is shunted to ground in the vicinity of the circuit rather than flowing through the power supply
circuitry. It is called a bypass capacitor.
The relationship between the diode “on” resistance and the DC quiescent current is determined
by taking the derivative with respect to vD of the diode equation for the special case when vD is
large enough to satisfy the approximation
i D  I S e vD / nVT .
This occurs when VD >> nVT, that is, when vD is greater than a few tenths of a volt. The
derivative is
 1  vD / nVT  1 
di D
e
 I S e vD / nVT .
 I S 
 
dv D
nV
nV
 T
 T


Note that the second quantity in parentheses on the right-hand side is the diode current (to a very
good approximation) under forward bias conditions. Thus,
di D
i
 D .
dv D nVT
The total current iD through the diode can be decomposed into its DC and AC parts as
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i D  I D  id ,
where ID is the DC quiescent (constant) average current and id represents the time-varying
component of the current (the AC variation). (This upper-case/ lower-case convention used to
distinguish between purely DC and purely AC signals is widely used in textbooks and technical
papers.) If the AC variation is small relative to the quiescent level (i.e., id << ID), then we can
make the approximation iD ≈ ID. Substituting this approximation and the definition
di D
1

dv D rd
into the expression for diD/dvD found above yields
rd 
nVT
.
ID
The thermal voltage VT is well defined (if the temperature is known), but n is an empirically
derived quantity. The value of n might be available on a datasheet, but more typically it must be
determined by measurement.
A circuit representation of the attenuator that is valid for small AC signals only is shown in
Figure 4. Note that resistor RB is depicted as grounded on one side. This is because of the bypass
capacitor in the actual circuit; it shorts one side of RB to ground with respect to AC signals. Also
note that the turn-on voltage VF of the diode is not included because it is a DC independent
source. It has no effect on the AC operation of the circuit. Employing an AC model like the one
in Figure 4 is akin to applying the principle of superposition and evaluating only the
contributions of the AC source (vg) to the voltages and currents in the circuit. All of the DC
voltage sources have been replaced with short circuits, as have the low-reactance capacitors.
Function
Generator
Rg
vg
+
−
rd
RB
+
vo
−
RL
Figure 4. AC representation of the attenuator circuit. Resistance Rg is the internal
resistance (the output resistance or Thévenin equivalent resistance) of the signal
source. The capacitors are not explicitly shown because they are assumed to be
shorts at the AC signal frequency. If RL >> rd and RB >> rd, then the value of rd
dominates the parallel combination of rd, RB, and RL.
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Experimental Procedure

Your task is to design and test an attenuator circuit like the one shown in Figure 3. The
bench-top function generator, which has an output resistance Rg of 50 , will serve as the AC
signal source. The generator voltage vg should be no more than approximately 100 mVpk to
ensure that the signal current through the diode is small relative to the DC (quiescent)
current. Remember: The amplitude displayed on the function generator’s screen is half
the value of the Thévenin equivalent voltage vg. You may use a very high resistor value for
RL (several hundred k, for example) so that the loading effect of RL can be ignored. Use a
1N914 or 1N4148 diode, and select a value for the DC blocking and AC bypass capacitors so
that they have less than 1  of reactance at 1 kHz and above. You will most likely have to
use electrolytic capacitors, so be sure to determine the proper orientation of each
capacitor in the circuit.
Your circuit should provide an attenuation setting of vo/vg = 0.10 when the control voltage
(the output of the scaling and level-shifting circuit you designed last week) is at its maximum
value of 11.75 V. When the control voltage is 0.5 V, there should be almost no attenuation
(i.e., vo ≈ vg). Base your design on the assumptions that rd << RL and rd << RB and that the
diode’s emission coefficient n is approximately 1.5. You will also need to assume a
reasonable approximation for the diode’s turn-on voltage VF. Consult the appropriate data
sheet for guidance. Also, remember to check the power dissipated by the various
components. If a component might have to dissipate more than its rated power, you must
devise a way to work around the problem. As part of your pre-lab work, you should have
completed Table 1 with predicted attenuation settings for all 16 control voltages.
Table 1. Attenuator specifications and operating parameters. The diode “on”
resistance should be based on an assumed value for n of 1.5.
Binary
Decimal
Control
Quiescent Diode Diode “On”
Attenuation
Number Equivalent Voltage (V)
Ratio
(vo/vg)
Current (A)
Resistance ()
0000
0
0.50
≈ 1.00
0001
1
1.25
0010
2
2.00
0011
3
2.75
0100
4
3.50
0101
5
4.25
0110
6
5.00
0111
7
5.75
1000
8
6.50
1001
9
7.25
1010
10
8.00
1011
11
8.75
1100
12
9.50
1101
13
10.25
1110
14
11.00
1111
15
11.75
0.10
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
Assemble your attenuator circuit, and connect it to the variable voltage circuit you designed
and built last week.

Use the oscilloscope to verify that your circuit is providing close to the specified amount of
attenuation at each control voltage setting. Try applying the “BW Lim” feature if there is a
lot of noise on the trace. Do not rely on the automatic voltage readings displayed on the
screen to record the various values of vo; the “fuzz” on the trace makes that feature useless.
Use the manual cursors instead.

[10 pts EXTRA CREDIT] If your results are consistently off in one direction for the higher
control voltage settings, consider the possibility that the estimated value for the emission
coefficient n that you assumed is incorrect. Devise a way to determine the value of n that
results in the best agreement between your target and measured attenuation levels, and use
the new value to revise your circuit design. Verify that your revised circuit is achieving the
target attenuation levels more closely. Report your initial and revised measurements.

Demonstrate your properly working circuit to the instructor or TA. Disagreements between
target and measured attenuations that are attributable to the wrong assumed value for n are
acceptable.

Capture screen images of the output voltage waveforms for the highest, lowest, and middle
(VS = 6.5 V, corresponding to binary 1000) attenuation settings to provide additional
evidence that your circuit is working properly. Include the screen images in your report with
appropriate discussions and any necessary annotations added. Be sure to include the value of
vg you used.
Grading
Each group must submit a brief but well written report that describes in detail all circuit design
choices, assembly steps, and the results of measurements. The report should include (but not
necessarily be limited to) all of the details requested in the “Experimental Procedure” section.
Pay especially close attention to the instructions and issues addressed in the “Lab Report
Guidelines” available at the lab web site. Issues that are specifically addressed in the
“Guidelines” will lead to larger grade penalties.
The report is due at the beginning of next week’s lab session. Each group member will receive
the same grade, which will be determined as follows:
10%
40%
30%
10%
10%
Pre-lab work: Copy of Table 1 with all blanks filled in
Demonstration of properly operating attenuator circuit
Report – Completeness and technical accuracy
Report – Organization, neatness, and style (professionalism)
Report – Spelling, grammar, and punctuation
© 2011-2012 David F. Kelley, Bucknell University, Lewisburg, PA 17837.
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