Open practice · AI allowed

Practice sheet: Chapter 5, The Operational Amplifier

This sheet is not marked for correctness, and AI tools are allowed. The device-free quiz at the start of week 11, session 1 (Thu 17 Dec), is built from twins of these questions, so make sure you can do each one on your own.

Two-tier items ask for an answer and a reason. Get both right; on the quiz each earns half the marks.
Predict first: where asked, make your prediction before you calculate.
Confidence: mark each question Sure or Unsure. It is not marked; it shows you what to revise.
Conventions: every op amp is ideal: no current enters either input, and with negative feedback in the linear region the two input voltages are equal ($v_n = v_p$). The output stays between the supply voltages; outside that range the op amp saturates. Voltages are measured from the ground symbol, and resistances are in kilohms, so currents come out in milliamperes. Check every answer: KCL at the inverting input must hold, and $v_o$ must lie between the supplies.

Prefer paper? Open the printable PDF.

Which questions practise which skill

1State the two ideal op-amp rules and when they apply S1 S4 S6 S7 S8 S11 S16
2Name an amplifier’s configuration from its circuit and write $v_o$ in terms of its inputs S1 S3 S5 S12 S13
3Analyse the inverting, summing, noninverting and difference amplifiers with KCL at the inverting input S2 S3 S4 S5 S6 S9 S11 S12 S13 S14 S15 S16
4Find the range of an input that keeps the op amp linear, and the output when it saturates S2 S3 S4 S5 S6 S8 S10 S13 S14 S15
5Find the current in a load and at the op amp’s output S7 S9
6Analyse two op amps in cascade and say which stage saturates first S10

S1Which configuration?Two-tier

What is this circuit, and what is $v_o/v_s$?

Answer

a)Inverting amplifier, −3b)Noninverting amplifier, 4c)Noninverting amplifier, 3d)Difference amplifier, 3

Reason

i)Every op-amp amplifier inverts, because the feedback goes to the inverting input.ii)The source drives the noninverting input; the feedback divider gives $v_n = v_o \times 5/(5 + 15)$, and $v_n = v_p = v_s$.iii)The gain is always the feedback resistance divided by the input resistance.iv)Any circuit with resistors on both inputs is a difference amplifier.

Follow-up: does the 10 kΩ resistor change the gain?

a)Yesb)No

S2The inverting amplifierPredict first

As in Nilsson Example 5.2.

a) Find $v_o$ for $v_s = 1.5$ V.

b) Find the current in the 24 kΩ resistor (its size)…

b) …and its direction.

a)From the inverting input toward the outputb)From the output toward the inverting input

c) What range of $v_s$ keeps the op amp in its linear region? Lowest $v_s$:

c) Highest $v_s$:

d) Predict first: what is $v_o$ for $v_s = 3$ V?

S3The summing amplifier

As in Nilsson Example 5.3.

a) Write $v_o$ in terms of $v_a$, $v_b$ and $v_c$, and find $v_o$ for $v_a = 1$ V, $v_b = 2$ V and $v_c = -1.5$ V.

b) With $v_a = 1$ V and $v_c = -1.5$ V, what range of $v_b$ keeps the op amp linear? Lowest $v_b$:

b) Highest $v_b$:

c) With $v_a = 2$ V, $v_b = 1$ V and $v_c = -1$ V, how large can the feedback resistor be before the op amp saturates?

kΩ

S4The noninverting amplifier

As in Nilsson Example 5.4.

a) Choose $R_s$ for a gain of 5.

kΩ

b) $v_g$ ranges from −2 V to +2.5 V. What are the smallest equal supply voltages ($\pm V_{CC}$) that keep the op amp linear? $V_{CC}$ =

c) What current flows in the 10 kΩ resistor?

c) What does that resistor do to $v_o$?

a)It lowers $v_o$b)It raises $v_o$c)Nothing: it does not change $v_o$

S5The difference amplifier

As in Nilsson Example 5.5.

a) Name the configuration…

a)Inverting amplifierb)Summing amplifierc)Noninverting amplifierd)Difference amplifier

a) …and write $v_o$ in terms of $v_a$ and $v_b$: $v_o = K(v_b - v_a)$ with $K$ =

V/V

b) Find $v_o$ for $v_a = 2$ V and $v_b = 2.8$ V.

c) With $v_b = 2.4$ V, what range of $v_a$ keeps the op amp linear? Lowest $v_a$:

c) Highest $v_a$:

S6Both inputs driven

As in Nilsson Example 5.1.

a) Find $v_o$ for $v_a = 2$ V and $v_b = 0$ V.

b) Repeat for $v_a = 2$ V and $v_b = 1$ V.

b) Why is $v_n$ no longer 0? What is it now?

c) With $v_a = 1.5$ V, what range of $v_b$ avoids saturation? Lowest $v_b$:

c) Highest $v_b$:

S7A buffer for a battery monitorPredict first

A 48 V solar battery bank can reach 60 V. A divider scales it down for a display that reads 0 to 5 V.

a) Without the op amp, the display is connected straight across the 10 kΩ. Predict first: will it read 5 V?

a)Yesb)No

a) Then find what it reads at 60 V.

b) With the op amp in place, what does the display read?

b) Why does the display no longer load the divider?

Work this out on paper, then compare with the explanation.

c) Where does the 0.5 mA in the display come from?

a)From the dividerb)From the op amp’s output, powered by its supplies

S8SaturationTwo-tier

An inverting amplifier has $R_s = 2$ kΩ and $R_f = 20$ kΩ, with supplies ±12 V. What is $v_o$ for $v_s = 1.5$ V?

Answer

a)+12 Vb)−15 Vc)−12 Vd)0 V

Reason

i)$v_o = -(R_f/R_s)v_s$ holds for every input.ii)A saturated op amp gives zero output.iii)The output cannot pass a supply voltage, so it stops at the negative supply.iv)A saturated op amp flips to the opposite supply.

Follow-up: while saturated, is $v_n$ still 0 V?

a)Yesb)No

Follow-up: find $v_n$.

S9The output current

a) Find $v_o$.

b) Find the current in the 3 kΩ load (its size)…

b) …and its direction.

a)Up from ground into the output nodeb)Down from the output node to ground

b) Find the current in the 12 kΩ resistor (its size)…

b) …and its direction.

a)From the inverting input toward the outputb)From the output toward the inverting input

c) Find the current at the op amp’s output terminal (its size)…

c) …and its direction.

a)Into the output terminal: the op amp sinks itb)Out of the output terminal: the op amp sources it

c) No current enters the inputs: why can the output carry current?

Work this out on paper, then compare with the explanation.

S10Two op amps in cascade

Both op amps use ±9 V supplies.

a) Find $v_{o1}$ for $v_s = 0.4$ V…

a) …and $v_{o2}$.

b) Repeat for $v_s = 2$ V: $v_{o1}$ =

b) $v_{o2}$ =

b) Which stage saturates?

a)The first stageb)The second stagec)Both stagesd)Neither stage

c) What range of $v_s$ keeps both stages linear? Lowest $v_s$:

c) Highest $v_s$:

S11Spot the errorSpot the error

The worked solution below finds $v_o$. It contains the kind of direction slip AI chat tools often make.

Assume the op amp is linear, so $v_n = v_p$ (this is checked in line 5).
$v_p = 1$ V, so $v_n = 1$ V.
The current from the 3 V source into the inverting node is $(3 - 1)/10 = 0.2$ mA.
It flows on through the 40 kΩ to the output, so $v_o = 1 + 0.2 \times 40 = 9$ V.
Check: 9 V lies inside ±15 V, so the op amp is linear and the answer stands.

b) Correct it and find $v_o$.

c) Check your answer with KCL at the inverting input.

Work this out on paper, then compare with the explanation.

d) Line 5 calls itself a check. Why does it prove nothing?

Work this out on paper, then compare with the explanation.

S12Spot the error in a difference amplifierSpot the error

This is a difference amplifier, so $v_o = (40/10)(v_b - v_a)$.
So $v_o = 4(2 - 1) = 4$ V.
Check: 4 V lies inside any usual supply range.

a) Which is the first wrong line?

a)Line 1b)Line 2c)Line 3

b) Find $v_p$…

b) …then $v_o$.

c) What resistor value at the noninverting input would make line 1 correct?

kΩ

S13Design a summing amplifier

Design a summing amplifier with $v_o = -(2v_a + 5v_b)$, using a 100 kΩ feedback resistor and ±12 V supplies.

a) Choose the input resistors. For $v_a$:

kΩ

a) For $v_b$:

kΩ

b) With $v_a = 1$ V, what range of $v_b$ keeps the op amp linear? Lowest $v_b$:

b) Highest $v_b$:

c) Find the current in the feedback resistor for $v_a = 1$ V and $v_b = 1$ V (its size)…

c) …and its direction.

a)From the inverting input toward the outputb)From the output toward the inverting input

S14Work backwards

a) Find $v_o$ when $R_x = 150$ kΩ.

b) How large can $R_x$ be before the op amp saturates?

kΩ

c) What happens to $v_o$ if $R_x$ is made larger still?

a)It keeps rising in proportion to $R_x$b)It stays at +10 V (saturated)c)It drops to 0 Vd)It flips to −10 V

S15From a sensor to a microcontroller

As in Nilsson’s Practical Perspective for this chapter. A temperature sensor gives 10 mV per °C, so 0 to 100 °C gives 0 to 1 V. The microcontroller’s analog input reads 0 to 5 V.

a) What gain maps 0–1 V onto 0–5 V?

V/V

a) Design a noninverting amplifier for it with a 40 kΩ feedback resistor: $R_s$ =

kΩ

b) The amplifier’s supplies are 0 V and +5 V. What does it output at 120 °C…

b) …and what temperature will the microcontroller report?

°C

c) A second sensor reads −20 °C to 80 °C, that is, −0.2 V to 0.8 V. Find $K$ and $L$ in $v_o = Kv_s + L$ that map this range onto 0–5 V. $K$ =

V/V

c) $L$ =

S16Check an answer without solving again

Two classmates report $v_o$. Student 1: $v_o = -3.5$ V. Student 2: $v_o = 4.5$ V. Use $v_n = v_p$ and KCL at the inverting input to decide which student is right.

First, $v_n$ =

Which student is right?

a)Student 1b)Student 2