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Class A BJT Amplifiers
62 questions By Tony R. Kuphaldt
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Question 55 of 62
Explain each of the mathematical approximations for this typical common-emitter amplifier circuit (with a bypass capacitor):
$$A_V \approx \frac{R_C||R_{load}}{r'_e}$$
$$Z_{in} \approx R_1 || R_2 || (\beta+1)r’_e$$
$$Z_{out} \approx R_C$$
What does each term in each expression represent, and why do they relate to one another as shown?
Reveal answerThe answers I leave for you to figure out!
Notes:The approximations for voltage gain, input impedance, and output impedance vary somewhat according to how precise the author(s) intended them to be. What you see here may be simpler or more complex than what you find in your textbook(s). The purpose of this question is to summarize gain and impedance calculations for this type of amplifier circuit, as well as to stimulate thought and discussion on the rationale for each. If students simply try to memorize these equations, they will forget them soon afterward. If they understand why each one is as it is from principles previously learned, both comprehension and retention will be much improved.
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Question 56 of 62
Explain each of the mathematical approximations for this typical common-emitter amplifier circuit (with the dynamic emitter resistance ßwamped” by RE):
$$A_V \approx \frac{R_C||R_{load}}{r'_e+R_E}$$
$$Z_{in} \approx R_1||R_2||(\beta+1)(r’_e+R_E)$$
$$Z_{out} \approx R_C$$
What does each term in each expression represent, and why do they relate to one another as shown?
Reveal answerThe answers I leave for you to figure out!
Notes:The approximations for voltage gain, input impedance, and output impedance vary somewhat according to how precise the author(s) intended them to be. What you see here may be simpler or more complex than what you find in your textbook(s). The purpose of this question is to summarize gain and impedance calculations for this type of amplifier circuit, as well as to stimulate thought and discussion on the rationale for each. If students simply try to memorize these equations, they will forget them soon afterward. If they understand why each one is as it is from principles previously learned, both comprehension and retention will be much improved.
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Question 57 of 62
A common set of equations for calculating input and output impedances of bypassed common-emitter amplifier circuits is as follows:
$$Z_{in} \approx R_1||R_2||(\beta+1)r’_e$$
$$Z_{out} \approx R_C$$
If precision is not required, we may greatly simplify the first equation by assuming the transistor to be ideal; i.e. having an infinite current gain (β = ∞). Re-write the first equation accordingly, and explain how you simplified it.
Reveal answer$$Z_{in} \approx R_1||R_2$$
Follow-up question: how does the similar simplification of the “swamped” common-emitter amplifier’s input impedance equation compare?
$$Z_{in} \approx R_1||R_2 || (\beta+1)(r’_e+R_E) \ \ \ \ \ \ \ \ Assuming \ \ a \ \ finite-beta \ \ transistor$$
Notes:The purpose of this question is for students to see how (more) approximate predictions for circuits may be obtained through simplification. A good exercise is to calculate impedances for a given amplifier circuit using both the original and the simplified equations, to see just how “approximate” the simplified answers are. Knowing how to eliminate complicated terms in equations (and what terms may be safely eliminated!) is key to estimating in the absence of a calculator.
