A two-stage amplifier has Stage 1 with an unloaded voltage gain of 50 and an output impedance of 8 kΩ, and Stage 2 with an input impedance of 2 kΩ. What is the actual overall voltage gain of the cascaded amplifier (ignoring Stage 2's own gain for simplicity)?
A50 — the stages multiply directly because coupling capacitors isolate them
B10 — the inter-stage voltage divider passes only 2/(8+2) = 20% of Stage 1's output to Stage 2
C100 — the two impedances add to increase the effective gain
D25 — you average the unloaded and loaded gains
Stage 2's input impedance loads Stage 1's output, forming a voltage divider: V_delivered = V_oc × [R_in2 / (R_out1 + R_in2)] = 50 × [2/(8+2)] = 50 × 0.2 = 10. This is the classic loading effect: the actual gain is far below the unloaded product because the stages interact through their impedances. Coupling capacitors block DC bias but do not isolate the AC signal path — impedances still interact at signal frequencies.
Question 2 Multiple Choice
Why is a common-collector (emitter follower) stage typically placed after a common-emitter gain stage rather than a second common-emitter stage?
AThe CC stage adds additional voltage gain that compensates for the loading loss
BThe CC stage's very low output impedance prevents the load from forming a damaging voltage divider with the CE output
CTwo CE stages would cancel each other's phase inversions, reducing net gain
DThe CC stage increases bandwidth more than a second CE stage would
The CE stage's output impedance (~R_C, often several kilohms) forms an unfavorable voltage divider with the external load resistance, wasting the gain achieved. The CC stage (emitter follower) has very low output impedance (typically tens of ohms) and near-unity voltage gain — it buffers the CE output so the load barely matters. Meanwhile, the CC stage's high input impedance doesn't significantly load the CE stage. This impedance matching is the core reason for the CE-CC configuration: CE provides gain, CC preserves it all the way to the load.
Question 3 True / False
Cascading three identical amplifier stages with individual −3 dB bandwidth of 1 MHz produces an overall −3 dB bandwidth narrower than 1 MHz.
TTrue
FFalse
Answer: True
Each stage's gain rolls off independently. At the individual stage's −3 dB frequency, each stage has already dropped by 3 dB, so three cascaded stages have dropped 9 dB total at that frequency — well past the combined −3 dB point. The combined bandwidth must be at a lower frequency, roughly 510 kHz for three identical stages (using the formula involving √(2^(1/n) − 1)). More stages always means narrower combined bandwidth — the gain-bandwidth tradeoff is inescapable.
Question 4 True / False
The overall voltage gain of a multi-stage amplifier equals the product of the individual stages' unloaded voltage gains.
TTrue
FFalse
Answer: False
This is the central misconception of multi-stage amplifier analysis. Each stage's output impedance loads the next stage's input impedance, forming a voltage divider at every interface. The correct formula is A_total = A1_loaded × A2_loaded × ..., where each stage's gain is computed with the subsequent stage's input impedance as the load. The unloaded gain product can be dramatically higher than the actual gain — in the extreme case where output impedance equals input impedance, each interface passes only half the signal, and the product of unloaded gains overstates actual gain by 2^(n-1) for n stages.
Question 5 Short Answer
Why does adding more stages to an amplifier inevitably narrow its overall bandwidth, and what design principle does this reflect?
Think about your answer, then reveal below.
Model answer: Each amplifier stage has its own frequency-dependent gain that rolls off above its −3 dB bandwidth. When stages are cascaded, their roll-offs compound: at any frequency where each stage contributes some gain reduction, the total reduction multiplies. The combined −3 dB point therefore falls at a lower frequency than any individual stage's bandwidth. For n identical stages, the bandwidth shrinks by a factor of √(2^(1/n) − 1). This reflects the fundamental gain-bandwidth product limitation: amplifier technology offers a fixed product of gain and bandwidth, so trading one for the other is unavoidable — more stages buy more gain but always at the cost of bandwidth.
The gain-bandwidth product is a device-level constraint rooted in transistor physics, but the compounding effect is a system-level consequence of the math of cascaded roll-offs. Engineers working around this use techniques like shunt-peaked loads or feedback to extend bandwidth per stage, but they cannot escape the underlying constraint — they can only shift where the tradeoff lands.