Small Signal Amplifiers Questions and Answers

Answer: A

A signal is small when the excursion is short enough that the curved characteristic can be replaced by its tangent without material error - for a bipolar device that means tens of millivolts at the base rather than any fixed figure. Frequency and power are separate considerations. The definition is about linearity rather than about magnitude in absolute terms, which is why the same amplitude can be small in one circuit and large in another. Most errors on this topic come from carrying a result across from a neighbouring scheme where it does not hold. Most errors on this topic come from carrying a result across from a neighbouring scheme where it does not hold.

Answer: B

Every element in the model is a derivative evaluated at one point, so moving the operating point changes them all - the transconductance most obviously, being proportional to the collector current. Test conditions are a data sheet matter, and the last option states a true fact about superposition without explaining the dependence. A linearisation is only as valid as the point it was taken about, which is why bias and signal analysis have to be done in that order.

Answer: C

The h-parameters describe the device as a two-port black box with an input impedance, a reverse voltage ratio, a forward current ratio and an output conductance. The voltage-controlled current source picture is the hybrid-pi model that largely replaced it. The black-box approach makes no assumption about the physics inside, which is its strength for measurement and its weakness for insight. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: D

Each hybrid-pi element maps onto something real - the transconductance to the operating current, the input resistance to beta, the output resistance to the Early effect - so the model explains as well as predicts. It has a comparable number of elements, is no easier to measure, and is just as restricted to small signals. A model whose parameters can be reasoned about is far more useful in design than one that can only be looked up. The shared properties explain why these schemes form a family, and the differences explain why more than one exists. The shared properties explain why these schemes form a family, and the differences explain why more than one exists.

Answer: A

The transconductance is the collector current divided by the thermal voltage, so it is fixed by the bias alone at about forty millisiemens per milliamp. Output resistance follows from the Early voltage and the current together, base spreading resistance is a bulk property, and the capacitance depends on the collector voltage. A parameter that depends only on the current the designer chose is the most predictable thing in the model, and most gain estimates are built on it.

Answer: B

The emitter resistance is the thermal voltage over the current:

\[ \begin{aligned} r_{e} &= \frac{26 \ \mathrm{mV}}{0.5 \ \mathrm{mA}} \\ &= 52 \ \Omega \end{aligned} \]

giving about 52 ohms, twice the value at a milliamp because the current is half. The inverse relation means halving the current doubles the resistance and halves the gain a given collector resistor can produce, which is why the operating current is a gain decision as well as a bias one.

Answer: C

The emitter resistance is reflected to the base multiplied by the gain:

\[ \begin{aligned} r_{\pi} &= \beta r_{e} \\ &= 200 \times 52 \\ &= 10.4 \ \mathrm{k\Omega} \end{aligned} \]

so about 10.4 kilohms, and the bias divider will usually be in parallel with it and may well dominate. Two quantities multiply here, one of which is unreliable, which is why input impedance is a far less predictable specification than gain. Most errors on this topic come from carrying a result across from a neighbouring scheme where it does not hold. Most errors on this topic come from carrying a result across from a neighbouring scheme where it does not hold.

Answer: D

Transconductance depends only on the operating current, whereas input resistance is beta times the emitter resistance and so inherits beta's threefold spread. Frequency and amplitude are separate matters, and the supply does not set the gain. A specification that avoids the unreliable parameter is worth trusting, and knowing which specifications do is part of knowing what a data sheet is telling you. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: A

The gain is minus the transconductance times the load, equivalently minus the collector resistance over the intrinsic emitter resistance. Beta does not appear, which is why the gain is predictable. The third option is the degenerated case with the emitter resistor unbypassed, and the fourth is not a gain expression at all. Two forms of the same result, one in conductance and one as a resistance ratio, and which is quicker depends on what the question supplies.

Answer: B

The emitter resistance in the denominator becomes the external resistor plus the intrinsic 26-ohms-per-milliamp figure, and since the external one usually dominates the gain becomes a resistor ratio. That is what makes it predictable and temperature-independent. The gain falls rather than being multiplied, and beta does not enter. Adding a term to a denominator is the algebraic signature of series feedback wherever it appears. Working one numerical case through both schemes side by side fixes the distinction better than any rule of thumb. Working one numerical case through both schemes side by side fixes the distinction better than any rule of thumb.