EE171L ver 0, 1
University of California, Santa Cruz
Baskin School of Engineering
Electrical Engineering Department
Analog Circuits Laboratory
EXPERIMENT 2: Small-Signal Diode Characteristics
I. Introduction
This laboratory experimentally determines two essential parameters found within the basic exponential diode
equation: ideality factor n, and saturation current or scale current . We will use the basic non-linear transfer
characteristics of a silicon junction diode to determine
and plot the measured
vs.
to show graphically the
diode’s inherent non-linear characteristic. Ideality factor n will be found by application of the small-signal model
where small-signal dynamic resistance
will also be observed experimentally. After completing this work, you
should have a thorough understanding of the non-linear volt-ampere relationship in the diode’s forward-bias region,
as well as how to operate the diode so a linear input-output relationship holds for small-signal applications.
II. General Circuit Discussion
Consider the following two will-known equations:
[1]
, where the thermal voltage
[2]
, dynamic ac small-signal diode resistance.
at room temperature.
The first equation describes the classic large-signal exponential relationship between the current through a junction
diode as a function of the voltage drop across it, while eqn.[2] is the small-signal dynamic (or AC) resistance the
diode exhibits when biased at a quiescent DC current
. Remember, this second equation is an approximation
holding only for small time-varying AC, or small-signal, inputs limited to about
in amplitude. The diode’s
current then varies nearly linearly with the small voltage changing across it, so we can treat the behavior of the diode
as a linear resistor having
Ohms – but only to the AC signal, not the DC bias
. Another way of
looking at this is to always remember that
is really a function of the instantaneous diode’s voltage and current,
and the small-signal condition approximates it as constant.
Fig. 1. Theoretical diode circuit.
Note: Re-draw this schematic in your engineering notes and make any experimental scribbles or annotations there.
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Fig. 1 shows the theoretical circuit that we want to implement experimentally. This will allow us to take accurate
measurements. Ideal voltage source
sets the DC bias point,
, in diode D in series with load resistor . The
AC small-signal from the signal generator,
is summed at node X with the DC bias voltage
capacitor C has the sole purpose of preventing any DC bias currents due to
. Blocking
from flowing back into the AC
source; it provides DC isolation so the summing junction X is truly the independent superposition of the AC and DC
signals.
Series resistor R allows us to accurately measure the diode’s small-signal reistance by forming a simple voltage
divider with . Fig.2 shows how this works with the equivalent small-signal AC circuit; the relevant voltage divider
equation is given by
[3]
, where
is considered negligibly small (how? By making C “large”).
Fig. 2.Theoretical small-signal equivalent circuit..
Note: Re-draw this schematic in your engineering notes and make any experimental scribbles or annotations there.
A practical implementation of the theoretical circuit is shown in Fig. 3 below.
Fig. 3. Practical circuit implementation.
Note: Re-draw this schematic in your engineering notes and make any experimental scribbles or annotations there.
The op-amps provide a convenient way to realize the necessary isolations indicated in the theoretical circuit.
functions as a unity-gain impedance buffer to isolate the unwanted effects of the signal generator’s output
impedance on the value of
.
is used in a similar manner: diode current
the measured resistance of
and the measured voltage drop across it for various settings or
effective resistance seen looking back into this branch would change whenever
will be found by calculation from
. Without
, the
was readjusted. Set he op-amp
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supply rails somewhere between 10 and 15Volts. Keep track of their actual values and make sure they remain stable
as you go through the experiment (don’t forget to bypass the supply pins). Finally,
is used as a 26 dB noninverting amplifier to extend the low voltage range input of the oscilloscope if necessary. Note the non-inverting
gain configuration was chosen instead of the inverting configuration to prevent shunt loading the diode by providing
a very high load impedance. The polarized blocking 6.8
capacitor was chosen have a very low reactance, so it
serves only to block DC and should have negligible effect on the AC voltage divider calculations noted in eqn. [2]; a
10
aluminum electrolytic will also work.
Take measurements to statistically estimate ideality factor n from a spread of different dynamic resistances and bias
current pairs. Tabulate your results and calculate the mean and standard deviation for n. Comment on these results.
Take DC measurements by varying the bias point to statistically estimate scale current
. Use the ideality factor
determined earlier in your calculations, and tabulate the DC data and results for each point used to determine the
mean and standard deviation of the scale current. Comment on these results.
Experimentally confirm that
does indeed represent a line tangent to each bias Q-point. Show this by first
producing and accurate plot of your experimental DC data of
extremes and one somewhere in the middle of the spread of
vs
. Then choose three points, two at the
(they must be actual measured values of
).
Accurately plot the dynamic resistance based on your graph’s x-y units and note how accurately they represent
tangent secant lines. We know how these lines should appear from theory, but here we want to see if the lines drawn
only from actual data confirm what we theoretically expect.
II. Procedure
1.
Determine the ideality factor n from different bias points using the small-signal equation [2].
A substitution procedure works best to accurately determine the dynamic resistance
. Using carefully
measured fixed resistors or a variable potentiometer (accurately measured for each setting used). Substitute
them for the diode and adjust the signal generator for a 1kHz small-signal sinusoidal output less than about 10
as measured at the output of
. This will provide the necessary small-signal ac input required by the
diode. Use op-amp
as a scope pre-amplifier if necessary (you can adjust the gain if necessary). With the
substitution resistor in place, let it be called
the output of
. Then replace
, measure the ac voltage across it with the scope and DVM at
with the diode and carefully adjust the Q-point bias current
the same small-signal ac voltage is obtained. Use Ohm’s law to find
. By substitution, it follows that
2.
from the drop across known resistor
which can then be used to find n from eqn. [2].
Determine the current and voltage characteristics for the diode in the forward-bias region to determine
the scale current .
Simply vary
law from
from about 5mV to 10.0 Volts and record
, and
,
, and
.
can then be found by Ohm’s
from eqn. [1] using the mean value of n you obtained in part 1 above. Be sure to take
enough points to construct an accurate graph of
3.
until exactly
vs.
.
Confirm suitability of the ac voltages used in the small-signal model.
Use the spectrum analyzer for this by qualitatively observing the harmonic content if a sinusoid greater than
10 kHz (so we can see the fundamental on the analyzer). If you leave
in the circuit, be sure to account for
any low-pass filtering effects due to its’ closed-loop gain-bandwidth product. Discuss whether you think the
nominal 10 mV amplitude is appropriate. Is it too high, low, very conservative, etc.