Output impedance with a resistor r across the constant

Question

Problem

Use SPICE to plot gain, magnitude and phase, for the following circuits as a function of frequency. Mark relevant points on the graphs for comparison with calculation of HW1. State the value(s) of frequency and gain at which the gain is real (Note that Gain = V_out/V_in is a complex quantity in general). Compare the results with your sketches of HW1.

For question 1 use a time constant for each stage of 39 µs and for 3 use a time constant for each network of 15.9 µs. For questions 2 and 4 choose a Q of about 10, and a resonant frequency of 10 kHz. Select reasonable, practical component values. For the graders convenience use a log frequency scale and gain in dB. Note that question 4 looks at a different output than in problem sets 1 and 2.

1. Three equal low pass filter stages.

2. Parallel resonant circuit.

3. Wien filter.

4. Series resonant circuit

5. Use the two diode model linearized as below

Where β = I_C/I_B is the current gain, and r_e is given by the diode equation (m=1) as 25mV_e at room temperature. Note: This is a linear model of the transistor. So we are assuming we have biased it at a suitable DC operating point which provides re as a known given value. When using a linearized model we are looking for an AC/small signal analysis.

With emitter grounded calculate

a) Input impedance at the base.

b) Output impedance at the collector

c) Output impedance with a resistor R across the constant current source (from the collector terminal to the base terminal) With base grounded calculate

d) Impedance at the emitter

e) Output impedance at the collector

f) Output impedance at the collector with a resistor R across the constant current source With an impedance R' to ground at the base

g) Impedance at the emitter