Physics 536 - Spring 2008
Electronic Techniques for Research
Example of Using Berkeley SPICE with nanoHUB
Frequency response of a common emittor amplifier
Consider the circuit shown below:
In which the components have the following values:
Component | Value |
VCC | 15 V |
VEE | 15 V |
Rin | 1 kΩ |
Cin | 0.1 μF |
Q1 | 2N3904 |
RB | 10 kΩ |
VB | 2.5 V |
RE | 500 Ω |
RC | 4 kΩ |
RL | 10 kΩ |
Cout | 0.1 μF |
The input to the amplifier is composed of the ideal AC voltage source
Vin(t) with impedance Rin and
the voltage source VB and RB
provide a bias voltage for the transistor. An equivalent circuit could
be constructed from a voltage divider between VCC
and VEE. The capacitors Cin
and Cout block the DC component of the input and
output voltages, but limit the low-frequency response to be
f-3 db=1/(2πRBCin)=160 Hz.
SPICE netlist
The SPICE netlist, including the
model for the transistor is as follows:
The AC response analysis results in the following output:
The low frequency cutoff is actually seen to be
f-3 db=200 Hz, which can be understood by considering
the actual input impedance of the amplifier to be
Zin = (1/RB + 1/(β RE))-1 = 8.3 kΩ
which gives
f-3 db(in)=1/(2π(Zin+Rin)Cin))=171 Hz
and by considering the low-frequency response of the output:
f-3 db(out)=1/(2π(RC+Rout)Cout)=113 Hz. The combination of high-pass filters at the input and the output
is effectively a second-order filter, which results in the higher -3 db cutoff
frequency found in the simulation.
High frequency response
With these component values, the high frequency cutoff is found to be
approximately f-3 db=6.6 MHz. Reducing RC
will reduce the gain, but also increases the high frequency cutoff:
AV | f-3 db |
-5 | 6.6 |
-4 | 8.7 |
-3 | 11.5 |
-2 | 15.1 |
This effect is caused by the parasitic capacitance in the transistor junction
between the collector and the base, which couples the amplified, but inverted,
signal at the collector directly to the base, cancelling the input signal.
The following modification to the circuit includes a second transistor in
a "cascode" configuration:
The second transistor shields the base of Q1 from the
amplified signal. The netlist
for this circuit gives the following frequency response:
and has the following dependence on the gain of the amplifier.
AV | f-3 db |
-5 | 14.5 |
-4 | 20.0 |
-3 | 26.3 |
-2 | 34.1 |