Differential Amplifiers Questions and Answers

Answer: A

A differential stage amplifies the difference between its inputs and, ideally, ignores whatever they have in common. The sum and the average both describe the common-mode component, which the stage is built to reject, and it does not select the larger. That one arrangement can amplify a wanted difference while discarding an unwanted shared signal is what makes it the input stage of nearly every precision analogue circuit. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: B

Any pair of inputs can be resolved into a common part, equal at both, and a differential part, equal and opposite - and the two are handled quite differently by the stage. Neither the supply midpoint nor a threshold enters into the definition. Resolving a pair of signals into these two components is the first step in every calculation here, and it works because the stage's response to each is independent.

Answer: C

The name comes from the large resistance, or in modern practice a current source, in the shared emitter tail, which is what forces the two devices to share a constant total current and so gives the stage its rejection. The collectors, the leads and the frequency response have nothing to do with it. A name describing the one component that makes an arrangement work is worth reading literally, since it points straight at the mechanism. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: D

A high-impedance tail fixes the sum of the two collector currents, so a common-mode input moves both devices together without changing anything at the outputs. The differential gain is set by the transconductance and the collector loads, base bias comes from the source impedance, and filtering is a separate function. Since the tail's impedance is what makes the common-mode gain small, it is the component that decides the rejection ratio. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: A

With a perfect tail nothing would move, but a real source has finite impedance, so both collectors shift slightly in the same direction and the difference between them stays near zero. Equal and opposite movement is the differential response. That the common-mode output appears at both collectors equally is precisely why taking the output differentially rejects it, and why a single-ended output does not reject it nearly so well. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: B

A differential input steers current from one device to the other, so one collector voltage rises exactly as much as the other falls. Movement in the same direction is the common-mode response. Because the total current is held constant by the tail, whatever one device gains the other loses, which is the mechanism behind both the differential gain and the doubling obtained by taking the output between the two collectors.

Answer: C

Each collector swings by the same amount in opposite senses, so the difference between them is twice either one's excursion. The tail current is constant by design, the input division is a separate matter, and the loads are not in series. A double-ended output also rejects the common-mode movement, since that appears equally at both, so the arrangement buys twice the gain and better rejection at once.

Answer: D

The ratio is the differential gain over the common-mode gain, usually quoted in decibels, and a hundred decibels means the stage amplifies a difference a hundred thousand times more than it amplifies a shared signal. Inverting it would give a number far below one, and neither a product nor a voltage difference is meaningful here. A figure of merit defined as a ratio of two gains compares the wanted response with the unwanted one directly, which is exactly what a specification should do.

Answer: A

Common-mode gain is roughly the collector load divided by twice the tail impedance, so a high-impedance tail makes it small and the rejection ratio large. The collector loads affect both gains and largely cancel out of the ratio, and neither current gain nor supply voltage is decisive. Replacing a tail resistor with a current source, whose impedance is hundreds of times higher, is the single most effective step towards good rejection and is why integrated pairs always use one.

Answer: B

Taking the ratio and converting:

\[ \begin{aligned} \text{CMRR} &= \tfrac{200}{0.02} = 10^{4} \\ &= 20\log_{10}10^{4} = 80 \ \mathrm{dB} \end{aligned} \]

giving 80 dB. The value 10000 is the ratio itself rather than its decibel form, and forty decibels would follow from the power convention, which does not apply to a ratio of voltage gains. Establishing whether a quantity is a power or an amplitude before converting is what settles the factor of two. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.