Op-amp technicalities

Question 1

What are the limits of op-amps? (5 limits, 1 outcome)

Answer 1

> Output voltage cannot exceed the supply voltages

> Input voltage cannot exceed the supply voltages

> Input voltage × Gain (G) cannot exceed supply voltages

> Differential input limit is the maximum difference between the V- and V+ inputs.

> The common-mode input voltage (the average between the two input voltages) cannot be too high.

> If limits are exceeded, the op-amp may start to draw significant current.

Question 2

What makes a system unstable?

Answer 2

When the output is not entirely controlled

Question 3

How does feedback impact a systems stability? What is the purpose of feedback?

Answer 3

> Feedback does not necessarily improve stability as an open-loop system is stable, but it is not very useful.

> Feedback allows us to control a system whilst maintaining stability.

Question 4

When does instability occur?

Answer 4

> When the phase of the feedback sifts by π radians (180°).

Question 5

What happens to the equations for the inverting and non-inverting amplifiers when instability occurs?

Answer 5

The denominators f both equations become 1 - AB.

Question 6

What are the 3 different cases of positive feedback signals?

Answer 6

> Small positive feedback: -1 < AB < 0

> Unstable system: AB = -1

> Large positive feedback: AB < -1

Question 7

What happens when there is small positive feedback?

Answer 7

• 1 + AB < 1 - G > A
• The system is not strictly unstable but it is approaching instability.
• The gain is increasing rapidly.
• G ⇒ ∞

Question 8

What happens when there is positive feedback and the system is unstable?

Answer 8

• 1 + AB = 0
• The equation becomes undefined (Does not apply anymore)
• Output is either at saturation at one of the supply voltages or has a self-sustaining oscillation

Question 9

What happens when there is large positive feedback?

Answer 9

> It would appear that the system would become stable again with a negative output, but this does not occur.

> Gain equations are no longer valid in the region beyond where G ⇒ ∞

Question 10

How does instability occur?

Answer 10

> Due to the design of an op-amp, there are several low pass filter stages in series

> Each low-pass stage produces an amplitude roll-off of 20dB/decade and a phase shift of -45° to 90° (at higher frequencies).

> Because they are in series, each phase shift acts on the preceding one.

> Eventually the phase shifts enough to cause positive feedback

Question 11

What is the solution that op-amps use to prevent instability?

Answer 11

> We use a low-pass filter which reduces at a relatively low frequency such that it dominates the frequency response.

> We force the open-loop gain to reduce to unity well before the phase shifts can accumulate to a critical -180°

> This is called dominant-pole frequency compensation

Question 12

What are the properties of the low pass dominant-pole frequency filter?

Answer 12

Roll off:

> 20dB/decade

> 6dB/ octave

> If we halve the signal frequency, then we will have twice as much open-loop gain Graph aspects:

> f_T = The point where the gain is unity

> GBP: Gain bandwidth product GBP = f_T

> GBW: Gain bandwidth GBW = f_T Gain constraint:

> The closed-loop gain (G) cannot exceed the open-loop gain (A) and so the closed-loop is bounded by the open-loop. If the gain that we want is greater than the open-loop gain then we have a gain error.

Question 13

What is phase margin?

Answer 13

> This is the difference between the total phase shift at f_T and the critical -180° phase shift.

> This is a measure of how close the op-amp is to instability at the transition frequency

> We need to ensure that we do not introduce any additional phase shifts externally to the op-amp

Question 14

Explain the different types of op-amp compensations

Answer 14

Fully compensated op-amp:

> The open-loop gain is rolled off to unity at a frequency where the phase shift is well below -180°

> This is done internally of the op-amp

Uncompensated op-amp:

> There is no in-built dominant-pole compensation

> The user is expected to add their own externally

Undercompensated op-amp:

> When the phase shift is at -180° the gain has not quite been rolled off to unity

> Intended to operate with a closed loop gain of 10 or more for high frequency circuits

> They are often called fast op-amps

> They are not stable at all

Question 15

How do you calculate the gain error?

Answer 15

1. Calculate the resistor configuration that will obtain the closed-loop gain that you wish to have
2. Calculate the value of B for that configuration
3. Decide what frequency you wish the op-amp to operate at
4. Use the response graph to calculate the open-loop gain (A) at that frequency
5. Insert the value of A and B into the gain equation for that type of op-amp and see what the actual gain becomes

Question 16

How can inverting and non-inverting op-amps produce a gain that is less than unity/

Answer 16

> By using gain error to their advantage

> this method is not recommended

Question 17

What can be said about the useful bandwidths of inverting and non-inverting amplifiers?

Answer 17

The useful bandwidth of the inverting configuration is only half that of the non-inverting configuration.

Question 18

What happens when you require a unity gain that is close to fT?

Answer 18

> You need to include the imaginary aspect of phase shifting

Non-inverting: G = -j / (1 + (-j × 1)) = -j / (1 - j)) G ≈ 1/√2

Inverting: G = -j0.5 / (1 - 0.5j) ≈ 0.45

> If the open-loop gain is large (you are not near f_T) then this does not matter

Question 19

Describe what can be said about choosing an op-amp based off fT?

Answer 19

> It is poor practice to design an op-amp circuit for operation close the f_T

> We also do not want to choose an op-amp with an excessively high fT

> 20dB gain can be ensured for: freq < 0.1f_T

Question 20

What is the issue with capacitive loads on op-amp circuits?

Answer 20

> Any load impedance which presents a capacitance between the output and ground introduces further phase shifting to the feedback path

Question 21

What is the definition of slew rate?

Answer 21

The limit for the rate of change of output voltage with time.

Question 22

Why will there be a limit to the slew rate?

Answer 22

Slew rate is limited by the finite internal current flow. An op-amp with a higher slew rate will draw more current from the power supply.

Question 23

How is the maximum slew rate requred calculated? What are its units?

Answer 23

Max slew rate = Aω

Differentiating the input signal: V = Asin(ωt) ⇒ dV/dt = Aωcos(ωt)

Units: V/s

Question 24

What is the problem if the slew rate is too large?

Answer 24

An op-amp with a very high slew rate may exhibit overshoot due to the combination of a fast output response and small but non-zero feedback delay.

Question 25

What is input bias current? When does it occur?

Answer 25

> Even though the impedance between the two inputs of an op-amp is very high, it is not infinite and so a very small current will flow between the inputs.

> Consequence 1: If there is a series capacitor on the input then it will accumulate a charge which will eventually saturate the output voltage.

> Consequence 2: A voltage error is added to input signal because there is a voltage across the impedance between the two inputs.

Question 26

How is input bias current prevented?

Answer 26

> Solution 1: Add a bias resistor between the input and ground. The problem with this is that this causes a high-pass filter on the input so you should pick the values of R_bias and capacitor accordingly.

> Solution 2: Ensure that the bias resistor is less than 1MΩ so we dont load the high resistance between the op-amp inputs

Question 27

What is the input offset voltage?

Answer 27

> A small internal offset voltage is added to the external differential input.

> This is due to the nature of how op-amps work

Question 28

What are the 2 consequences and two solutions to input offset voltage?

Answer 28

> Consequence 1: If the difference between the two inputs is very small ≈ 0 then this bias voltage is enough to cause the output to saturate.

> Solution 1: When using negative feedback this stops the input offset from affecting the output.

> Consequence 2: When using negative feedback, the output voltage will be offset from ground when the input is at reference voltage (e.g. 0V).

> Solution: There are offset pins that allow the designer to compensate for the offset voltage by including a potentiometer between the compensation pins and the negative supply voltage. But it is advisable to ignore this technique wherever possible because thermal drift will make the compensation ineffective.

Question 29

Define “Power-supply-rejection-ratio”

Answer 29

The ability of an op-amp to reject fluctuations on power supply rails.

Question 30

What is the problem with fluctuations in the power supply rails?

Answer 30

> It can cause instability

> Small high-frequency signals can be added to the op-amp output

Question 31

How can variations in supply voltage be removed externally?

Answer 31

> Using bypass capacitors between each supply and ground (or reference voltage) to lower the resonant frequency added by the supply.

> The type of capacitor is more important than its value

• Ceramic or polyester capacitors are preferred.
• 100nF is normal

> Inductance in power supply wires often makes it worse so keep wires short

Question 32

What are the equations for PSRR? What are the units?

Answer 32

PSRR = ∆V_diff / ∆V_PSU

PSRR = -20Log(∆V_diff / ∆V_PSU)

Units: μV/V or dB

Question 33

What is thermal noise performance?

Answer 33

> Main source of noise in op-amps

> Noise power is proportional to both temperature and bandwidth.

> Function of resistance (External resistors will add thermal noise)

> Units V/√Hz

Question 34

What is thermal drift?

Answer 34

> The characteristics of the op-amp will change depending on the temperature of the device.