Differential Amplifiers Questions and Answers

Q: Over roughly what input difference is a bipolar pair linear?

The transfer characteristic is a hyperbolic tangent, and it departs from a straight line well before the twenty-six millivolt thermal voltage is reached, so a few tens of millivolts is the practical limit. A few volts would be far into full steering, and microvolts would be an unnecessarily narrow claim. Emitter degeneration widens the linear range at the cost of gain, which is exactly the trade a single-ended stage makes for the same reason. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Q: How is a pair's linear input range widened?

Resistors in the two emitters apply local feedback exactly as they do in a single-ended stage, reducing the gain and extending the range over which the transfer is straight. A larger tail current raises the transconductance and narrows the range in millivolt terms, larger loads raise the gain, and common-mode range is a separate specification. Trading gain for linearity through series feedback is the same move in every topology. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Q: What is the transfer characteristic of a bipolar differential pair?

The two exponential characteristics combine into a hyperbolic tangent, which is linear near the origin and saturates at full steering in both directions. A field effect pair follows a square-law-derived shape instead, and neither a straight line nor a bare exponential describes it. That the saturation is smooth rather than abrupt is what lets the same circuit serve as a linear amplifier near the origin and as a limiter further out. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Q: Why does a differential pair make a good multiplier element?

The transconductance is proportional to the tail current, so a signal applied differentially is multiplied by whatever the tail current is made to represent - which is the basis of the Gilbert cell and of every analogue multiplier and balanced mixer. Offset, input impedance and output arrangement are not what makes it work. A stage whose gain is set by a current is a multiplier waiting to be used, and recognising that turns one circuit into a whole family. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Q: A pair's tail current is doubled from \( 1 \ \mathrm{mA} \) to \( 2 \ \mathrm{mA} \). Its differential gain

Each device now carries a milliamp rather than half of one:\[ g_{m} = \frac{I_{C}}{V_{T}} \propto I_{C} \]so the transconductance and hence the gain double, for the same collector loads. The linear input range narrows in proportion, and the dissipation doubles. One parameter change moving gain, linearity and power in predictable directions is what makes the tail current the principal design lever in this stage.

Q: Why is offset always referred to the input?

Referring an imperfection to the input divides out the gain, so two amplifiers of different gain can be compared on the same footing. It is actually harder to measure there, which is why it is computed from an output measurement. The mismatch does occur at the input but that is not why the convention exists. Referring an error to the input is a general technique that works because everything at the input is multiplied by the same gain as the signal. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Q: Which of the following is not a differential pair specification? Pinch-off voltage Input offset voltage Common-mode rejection ratio Input bias current

Pinch-off voltage describes a junction field effect transistor's channel closing and is a device parameter rather than a property of the pair. The other three are standard specifications for any differential input stage, bipolar or field effect. Spotting a parameter that belongs to one device family, appearing in a list of circuit-level specifications, is a quick way to identify the odd one out.

Q: The figure comparing a stage's differential gain with its common-mode gain is the common-mode ______ ratio.

This is the common-mode rejection ratio, and it should be large - a hundred decibels is good. Conversion describes what a mismatch does when it turns common-mode into differential, transfer would suggest the opposite of rejection, and feedback is a different concept entirely. A figure of merit whose name says what the circuit does well, and which grows as the circuit improves, is one worth reading literally.

61.

Over roughly what input difference is a bipolar pair linear?

A.A few tens of millivolts
B.A few volts
C.A few microvolts
D.A few hundred volts

Answer: A

The transfer characteristic is a hyperbolic tangent, and it departs from a straight line well before the twenty-six millivolt thermal voltage is reached, so a few tens of millivolts is the practical limit. A few volts would be far into full steering, and microvolts would be an unnecessarily narrow claim. Emitter degeneration widens the linear range at the cost of gain, which is exactly the trade a single-ended stage makes for the same reason. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

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62.

How is a pair's linear input range widened?

A.A wider input common-mode range
B.Emitter degeneration resistors
C.A larger tail current source
D.Higher collector load resistances

Answer: B

Resistors in the two emitters apply local feedback exactly as they do in a single-ended stage, reducing the gain and extending the range over which the transfer is straight. A larger tail current raises the transconductance and narrows the range in millivolt terms, larger loads raise the gain, and common-mode range is a separate specification. Trading gain for linearity through series feedback is the same move in every topology. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

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63.

What is the transfer characteristic of a bipolar differential pair?

A.A square law in the input difference
B.An exponential in the input difference
C.A hyperbolic tangent of the input difference
D.A straight line over the whole input range

Answer: C

The two exponential characteristics combine into a hyperbolic tangent, which is linear near the origin and saturates at full steering in both directions. A field effect pair follows a square-law-derived shape instead, and neither a straight line nor a bare exponential describes it. That the saturation is smooth rather than abrupt is what lets the same circuit serve as a linear amplifier near the origin and as a limiter further out. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Discuss in Forum

64.

Why does a differential pair make a good multiplier element?

A.Its offset voltage is very small
B.Its input impedance is very high
C.Its output is always single-ended
D.Its gain is proportional to the tail current

Answer: D

The transconductance is proportional to the tail current, so a signal applied differentially is multiplied by whatever the tail current is made to represent - which is the basis of the Gilbert cell and of every analogue multiplier and balanced mixer. Offset, input impedance and output arrangement are not what makes it work. A stage whose gain is set by a current is a multiplier waiting to be used, and recognising that turns one circuit into a whole family. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Discuss in Forum

65.

What is a balanced mixer built from a differential pair used for?

A.Multiplying two signals to shift a frequency
B.Amplifying a difference with high rejection
C.Comparing two voltages and switching
D.Regulating a supply against load changes

Answer: A

Driving the tail with one signal and the bases with another multiplies them, producing sum and difference frequencies while suppressing both inputs at the output - the frequency conversion every superheterodyne receiver needs. Amplification, comparison and regulation are other uses of related circuits. That suppressing the inputs at the output falls out of the balance, rather than needing a filter, is why the arrangement is called balanced and why it displaced the simple mixer.

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66.

A pair's tail current is doubled from \( 1 \ \mathrm{mA} \) to \( 2 \ \mathrm{mA} \). Its differential gain

A.Quadruples
B.Doubles
C.Halves
D.Is unchanged

Answer: B

Each device now carries a milliamp rather than half of one:

\[ g_{m} = \frac{I_{C}}{V_{T}} \propto I_{C} \]

so the transconductance and hence the gain double, for the same collector loads. The linear input range narrows in proportion, and the dissipation doubles. One parameter change moving gain, linearity and power in predictable directions is what makes the tail current the principal design lever in this stage.

Discuss in Forum

67.

A pair with \( 100 \ \mathrm{\mu V} \) offset and a gain of \( 1000 \) shows an output offset of

A.1 V
B.10 mV
C.100 mV
D.100 microvolts

Answer: C

Input-referred offset is multiplied by the gain on its way to the output:

\[ 100 \times 10^{-6} \times 1000 = 100 \ \mathrm{mV} \]

giving 100 millivolts, which in a high-gain stage can be a large fraction of the available swing. That a microvolt-level imperfection becomes a substantial output error is exactly why offset is referred to the input, and why it is the specification that limits precision direct-coupled measurement.

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68.

Why is offset always referred to the input?

A.It is easier to measure at the input than the output
B.The input is where the mismatch physically occurs
C.The output offset cannot be measured accurately
D.It makes the figure independent of the gain

Answer: D

Referring an imperfection to the input divides out the gain, so two amplifiers of different gain can be compared on the same footing. It is actually harder to measure there, which is why it is computed from an output measurement. The mismatch does occur at the input but that is not why the convention exists. Referring an error to the input is a general technique that works because everything at the input is multiplied by the same gain as the signal. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Discuss in Forum

69.

Which of the following is not a differential pair specification?

Pinch-off voltage

Input offset voltage

Common-mode rejection ratio

Input bias current

A.Pinch-off voltage
B.Input offset voltage
C.Common-mode rejection ratio
D.Input bias current

Answer: A

Pinch-off voltage describes a junction field effect transistor's channel closing and is a device parameter rather than a property of the pair. The other three are standard specifications for any differential input stage, bipolar or field effect. Spotting a parameter that belongs to one device family, appearing in a list of circuit-level specifications, is a quick way to identify the odd one out.

Discuss in Forum

70.

The figure comparing a stage's differential gain with its common-mode gain is the common-mode ______ ratio.

A.feedback
B.rejection
C.conversion
D.transfer

Answer: B

This is the common-mode rejection ratio, and it should be large - a hundred decibels is good. Conversion describes what a mismatch does when it turns common-mode into differential, transfer would suggest the opposite of rejection, and feedback is a different concept entirely. A figure of merit whose name says what the circuit does well, and which grows as the circuit improves, is one worth reading literally.

Discuss in Forum

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