ELEC 350L
Electronics I Laboratory
Fall 2011
Lab #8: Diode-Based Attenuator
Introduction
The piecewise linear model of the pn-junction diode under forward bias conditions includes a
resistor in series with an independent voltage source. The value of the series resistance depends
on the diode current, a property that can be exploited to design a remotely controlled attenuator
circuit. Attenuation is a reduction in signal strength. It can be undesirable, as in the case of long
distance radio communication, or it can be introduced on purpose to protect sensitive equipment
from strong signals or to implement a volume control, among other uses. In this lab exercise you
will design and test a simple attenuator and use it to control the amplitude of a sinusoidal signal.
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 iD is the diode current flowing 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 saturation current, and the constant n is the emission coefficient, the
value of which varies between one and two for most silicon diodes. The constant VT is the
thermal voltage, given by
kT
T
,
VT 

q 11,600
where T is the temperature in Kelvin; 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.
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 1, and the actual i-v
characteristic represented 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. If
the diode current fluctuates significantly, it might be pointless to determine the value of rd since
it too would fluctuate. However, in the case where the current varies little 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.
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iD
slope = 1/rd
vD
VF
Figure 1. 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 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 2. Resistor RB is chosen to establish a “quiescent,” or average, DC current
flowing through the diode. The time-varying signal coming from the function generator is
assumed to be weak enough so that the current it causes to flow through the diode is a tiny
percentage of the DC current. Thus, the diode’s “on” resistance rd is not significantly affected by
the signal current.
C
VS
Function
Generator
Rg
vg
+
−
RB
C
C
+
vD
−
iD
+
vo
−
RL
Figure 2. 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.
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The two capacitors connected to the anode of the diode in Figure 2 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
The value of C is chosen so that the reactance is insignificant compared to Rg and rd at the lowest
frequency of interest (where XC is greatest in magnitude). The capacitor in parallel with the
power supply VS ensures that any signal energy that gets past 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 derivate 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 .
The derivative is
 1
di D
 I S 
dv D
 nVT
 vD / nVT  1 
e
 I S e vD / nVT .
 

 nVT 


Note that the second quantity in parentheses on the right-hand side is the diode current. Thus,
di D
i
 D .
dv D nVT
Recall that the slope of the curve is equal to the reciprocal of the diode’s on resistance rd.
Furthermore, if the AC variation around the DC quiescent level of the current is small, then we
can make the approximation iD ≈ ID, where upper-case variables are used here to represent
constant quantities (like DC currents), and lower-case variables represent time-varying
quantities. By the way, this lower-case/upper-case convention is widely used in textbooks and
technical papers. Making these two substitutions 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 AC signals only is shown in Figure 3.
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
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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 3 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 3. AC representation of the attenuator circuit. Resistance Rg is the internal
resistance (the output resistance or Thévenin equivalent resistance) of the signal
source. If RL >> rd and RB >> rd, then the value of rd dominates the parallel
combination of rd, RB, and RL.
Experimental Procedure

Your primary task is to design an attenuator circuit like the one shown in Figure 2. The AC
signal source will consist of the bench-top function generator. You will need to determine the
output resistance Rg of the generator. (You may use the value specified in the manual or
somewhere else.) 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 not
the value of vg. You may use a very high value for RL (several hundred k, for example) so
that the loading effect of RL can be ignored. Use a 1N914 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 have to use electrolytic capacitors. You must therefore determine the
proper orientation of each capacitor in the circuit. For consistency among lab groups, use
a power supply voltage of VS = 15 V.
Your circuit should be able to provide the following five attenuation settings, selectable by
some kind of switching arrangement:
vo/vg = 0.10, 0.25, 0.50, 0.75, 1.00
You should find that you cannot complete the design without knowing the value of the
diode’s emission coefficient n. For now, assume that n = 1.
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A suggested circuit for switching between the various required quiescent diode current levels
is shown in Figure 4. You may devise an alternate switching circuit, if you wish. Remember
to check the power dissipated by the various components.
S1
to VS in
Fig. 2
R1
S2
R2
S3
R3
S4
R4
R5
to anode
in Fig. 2
Figure 4. Suggested switching circuit to provide adjustable quiescent diode
currents in the attenuator circuit. This circuit replaces the single resistor RB in
Figure 2; that is, it implements a five-step selectable resistance.

Use the oscilloscope to verify that your circuit is providing close to the specified amount of
attenuation at each 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; the “fuzz” on the trace makes that
feature useless. Use the manual cursors instead. Use your results to estimate the value of n
for your diode, and, if necessary, revise your design to match the attenuation specifications.
Once that is done, verify that your revised circuit is working correctly.

Demonstrate your properly working circuit to the instructor or TA.

For each attenuation setting, capture the screen image of the output voltage waveform.

On a separate sheet(s) of paper, provide copies of the screen captures of the output
waveforms for all setting. For each case include the value of vg expressed in units of mVpk.
Also include a table with the following information for each of the target attenuation (vo/vg)
settings: quiescent current level, calculated diode on resistance, RB (i.e., the total currentlimiting resistance), and measured attenuation. Finally, include a sketch of your resistance
switching network with resistor values.
Grading
Notebook entries will be assigned grades according to the criteria outlined in the “Policies and
Grading Guidelines.” Notebooks must be submitted by 5:15 pm on the day of the lab session.
The lab performance grade will be assigned according to the following guidelines. Each lab
group member will receive the same grade.
30%
30%
40%
Efficient and effective resistor switching network designed to meet specifications
Quality of performance summary table
Properly operating attenuator circuit
© 2011 David F. Kelley, Bucknell University, Lewisburg, PA 17837.
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