EXPERIMENT 3
SILICON DIODES
OBJECTIVE
To study the characteristics and applications of silicon diodes.
THEORY
Diodes are nonsymmetrical electrical devices. They conduct better when one end, called
the anode, is positive with respect to the other end, called the cathode. Physical diodes are often
marked with a line, like a minus sign, at the cathode, signifying that the diode will conduct better
when this end is more negative than the other end. The symbol for a diode contains an arrowhead
pointing from the anode to the cathode, which is the direction in which the current preferentially
flows.
There are several useful approximations to describe the operation of diodes in circuits:
1) Crude. The diode is a short circuit, like a closed switch, when voltage is applied in the
forward direction, and an open circuit, like an open switch, when the voltage is applied in the
reverse direction. This is also called the "ideal diode" approximation, and is usually a good
starting point in understanding a new circuit.
2) Standard. The diode is a 0.7 volt source, with no series resistance, when voltage is
applied in the forward direction, and an open circuit when the voltage is applied in the reverse
direction. This somewhat better approximation tries to account for the voltage drop across the
diode when current is flowing through it in the forward direction by saying that the voltage
across the diode is always exactly 0.7 volts.
3) Theoretical. Theoretically, the current through many silicon diodes at room
temperature is related to the voltage across them by the equation
- 10 -
V
kTV
26 mV
I = I0 e − 1 ≈ I0 e
(3 − 1)
where k is Boltzman’s constant, T is the absolute temperature, and Io is the “leakage” current
when the diode is reverse biased. This approximation implies a theoretical value for the
differential resistance of the forward conducting diode. The differential resistance of the diode, r,
which is also called the "ac" resistance, relates the change in voltage to a change in current:
rd =
δV
δI
(3 − 2 )
where δV and δI are small changes in the voltage and current in the diode from its operating
point. For many silicon diodes at room temperature r is given approximately by
r=
26 mV
ohms
I
(3 − 3)
where I is the current in amps flowing through the diode. This resistance is often only a few
ohms. It is in series with the 0.7 volts already present in the standard approximation.
The current - voltage characteristics of the three models are shown with the figures.
PROCEDURE
- 11 -
1) Connect the circuit in Fig. 1, and apply voltages varying from -10 to 10 volts to the
input, in one volt increments. With the digital voltmeter, measure and record the output voltages.
How do your results compare with the crude approximation? How do they compare with the
standard approximation?
2) Connect the circuit in Fig. 2, and apply voltages from -10 to 10 volts to the input, in
one volt increments. With the digital voltmeter, measure and record the output voltages. Since
the output does not change much, be sure to measure to three significant figures. How do your
results compare with the crude approximation? How do they compare with the standard
approximation?
3) Connect the circuit in Fig. 3 and apply voltages from -2 to 2 volts to the input, in 0.2
volt increments. With the digital voltmeter, measure and record the output voltages, again to 3
significant figures. This circuit is called a "limiter." It permits small input voltages to pass
without attenuating them at all, but it limits the output to at most about ± 0.7 volt with large
input voltages. Note that in the crude approximation this circuit would not work at all; the two
ideal diodes "back to back" would simply constitute a short to ground and the output would
always be zero.
ASSIGNMENT
Using your measurements for Figs. 1, 2, and 3, plot the output voltages, (Y axes), as a
function of the input voltages, (X axes). On the same plots, show the outputs that would be
expected in the crude and standard approximations.
Use the data from the part 2 to compute the current flowing through the diode. This is the
same as the current flowing through the 1 kΩ resistor, since there is no place else for that current
to flow. The current through the 1 kΩ resistor may be computed, using Ohm's law, from
- 12 -
I=
(Vin − Vout )
1 kΩ
(3 − 4 )
Plot the current flowing through the diode (Y axis) as a function of the output voltage,
which is the voltage across the diode (X axis). On the same plot show the current - voltage
relationship expected in the standard approximation. What is the maximum voltage difference
between your experimental data and the standard approximation?
Using the same data, compute the differential resistance of the diode from equation (3-2)
by taking differences between successive data points for ∆V and ∆I. Plot the differential
resistance (Y axis) as a function of the current (X axis) through the diode. The current used in
this plot should be the average of the two successive values that form ∆I. For comparison, also
plot equation (3-3) on the same graph. How does your plot of differential resistance compare
with the theoretical approximation in equation (3-3)?
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