Operational Amplifiers

Question 1

What are the 3 configurations for OpAmps?

Answer 1

> Non-inverting

> Inverting

> Schmitt Trigger

Question 2

What are the features of the OpAmp component?

Answer 2

> 2 Inputs, Inverting (+) and non-inverting (-)

> 1 Output

> Gain, Symbol A

Question 3

What is an important aspect of the inputs?

Answer 3

> They draw no current

> They are ‘virtually’ shorted together

Question 4

What can be said about the gain of an amplifier?

Answer 4

Infinite.

Only limited by the power-supply

Question 5

What is the simplification of an OpAmp?

Answer 5

A voltage controlled ideal voltage source.

Controlled by the voltage different between the inverting and non-inverting input.

Question 6

What is the equation for the output voltage of an OpAmp?

Answer 6

Vout = A(V[+] - V[-])

Question 7

What is the configuration of a non inverting amplifier?

Answer 7

A potential divider between the output of the OpAmp and ground with the output of the potential divider as the inverting input (-). The non-inverting input is the input voltage to the circuit.

Question 8

What is the equation for a non-inverting amplifier?

Answer 8

Vout = V[+] × (R1 + R2)/R2

Question 9

What is the concept of negative feedback?

Answer 9

If the gain of the amplifier changes, the circuit will counteract this by changing the voltage on the inverting input so the output voltage remains balanced.

Question 10

What happens on a non-inverting amplifier if the input voltage is constant but the gain increases?

Answer 10

1. The gain increases
2. The output voltage increases
3. The output voltage is fed back into the inverting input and this is therefore increased
4. This will cause the difference between the inputs to become smaller causing the output voltage to decrease

> This balances the output voltage

Question 11

How can the equation for a non-inverting amplifier be derived?

Answer 11

Vout = A(V[+] - V[-])

V[-] = Vout × R2/(R1 + R2)

Vout = A(V[+] - Vout × R2/(R1 + R2))

Vout = AV[+] - AVout × R2/(R1 + R2)

Vout + AVout × R2/(R1 + R2) = AV[+]

Vout (1 + A × R2/(R1 + R2) = AV[+]

Vout = AV[+]/(1 + A × R2/(R1 + R2)

Vout = AV[+]/(A × R2/(R1 + R2)

Vout = V[+]/(R2/(R1 + R2)

Vout = V+/R2

Question 12

What is the configuration of an inverting amplifier?

Answer 12

Non-inverting input is connected to ground. Resistor is connected between output and inverting input (R2). Resistor is connected between voltage input and inverting input (R1).

Question 13

What is the equation for the inverting amplifier?

Answer 13

Vout = -(R2/R1)Vin

Question 14

What is the concept of ‘virtual’ ground?

Answer 14

Because the non-inverting input is connected to ground and there is a ‘virtual’ short between the two inputs this means that the inverting input is ‘virtually’ connected to ground and so when calculating voltages this needs to be taken into account.

Question 15

How can we derive an equation for Vout for an inverting amplifier?

Answer 15

Vout = A(V[+] - V[-])

Vout = A(0 - V[-]) = -AV[-]

V[-] = -Vout/A

i = Vr1/R1 = (Vin - V[-])/R1

i = Vr2/R2 = (V[-] - Vout)/R2

i = i

(Vin - V[-])/R1 = (V[-] - Vout)/R2

(Vin + Vout/A)/R1 = (-Vout/A - Vout)/R2

(AVin + Vout)/R1 = (-Vout - AVout)/R2

AVin/R1 + Vout/R1 = -Vout/R2 - AVout/R2

AVin/R1 = - Vout/R1 -Vout/R2 - AVout/R2

AVin = - Vout -VoutR1/R2 - AVoutR1/R2

AVin = (-VoutR1/R2)(1+A) -Vout

AVin = (-VoutR1/R2)A -Vout

AVin = (-VoutR1/R2)A

{because A is so large Vout can be ignored}

Vin = -VoutR1/R2

Vout = -VinR2/R1

Question 16

What is the configuration for an inverting schmitt trigger?

Answer 16

The same as a NON-inverting amplifier but with the input terminals the opposite away around. The non-inverting input is on the potential divider

Question 17

What is positive feedback?

Answer 17

If the gain increases, this causes a chain of events that causes the output to runaway and become saturated

Question 18

What is the chain of events for positive feedback?

Answer 18

1. Gain increases
2. The output voltage increases
3. The non-inverting input voltage increases
4. This will cause the output voltage to increase even more
5. The non-inverting input will therefore increase more
6. Eventually this process repeats until the source voltage (maximum voltage) is reached.

Question 19

When the maximum voltage of a schmitt trigger is reached, what is this called?

Answer 19

The saturation voltage

Question 20

For an inverting schmitt trigger, what happens when the non-inverting input is larger than the inverting input?

Answer 20

The output of the schmitt trigger will be at positive saturation.

Question 21

For an inverting schmitt trigger, what happens when the non-inverting input is smaller than the inverting input?

Answer 21

The schmitt trigger will be at negative saturation.

Question 22

What is the behavior of the inverting schmitt trigger in all different scenarios?

Answer 22

When: Sat+ < Vin ⇒ Sat-

When: Sat- > Vin ⇒ Sat+

Question 23

What is the equations for the threshold voltages for the inverting schmitt trigger?

Answer 23

V+ = VsatR1/R2+R1

V+ = -VsatR1/R2+R1

Question 24

What is the configuration of the non-inverting schmitt trigger?

Answer 24

An inverting schmitt trigger but with the inputs reversed. Inverting input is connected to ground.

Question 25

How does a non-inverting schmitt trigger work?

Answer 25

If the input is greater than 0V then the output will be at positive saturation. If the input is lesser than 0V then the output will be at negative saturation.

Question 26

How does the process for reaching positive saturation work for a non-inverting schmitt trigger?

Answer 26

1. The input voltage is positive 2. The output voltage will be positive 3. This will cause the input voltage to increase 4. This will cause the output voltage to increase 5. This will cause the input voltage to increase further 6. This will repeat until the output voltage reaches positive saturation

Question 27

How does the process for reaching negative saturation work for a non-inverting schmitt trigger?

Answer 27

1. The input voltage is negative 2. The output will therefore be negative 3. This will cause the input voltage to decrease 4. This will cause the output voltage to decrease 5. This will cause the input voltage to decrease further 6. This will repeat until the output voltage reaches negative saturation

Question 28

What are the different types of filters and what do they do?

Answer 28

Low-pass filter: Cur out frequencies above a threshold High-pass filter: Cut out frequencies below a threshold Band-pass filter: Only allows frequencies between two points Band-stop filter: Cuts out frequencies between two points

Question 29

What is a Twin-T notch filter?

Answer 29

A band-stop filter

Question 30

What is the configuration for a Twin-T notch filter

Answer 30

Question 31

What is the most important design parameter? What is the equation for it?

Answer 31

Notch frequency f = 1/2πRC

Question 32

What are 2 important parameters for designing a twin-t notch filter?

Answer 32

R1 \< R2 \<\< R Q = R2/4R1

Question 33

With regards to a twin-t notch filter what is Q?

Answer 33

This is quality factor. It is an important consideration when designing a twin-t filter

Question 34

What is the equation to calculate the output voltage of a differential amplifier? How is it derrived?

Answer 34

Short across V2: I1 = If V1/R1 = -Vout/R3 Vouta = -V1 × R3/R1 Short across V1 V+ = V2 × R4/(R2 + R4) V- = Vout × R1/(R1 + R3) V+ = V- Voutb × R1/(R1 + R3) = V2 × R4/(R2 + R4) Voutb = V2 × R4/(R2 + R4) × (R1 + R3)/R1 Vout = Vouta + Vout b Vout = V2 × R4/(R2 + R4) × (R1 + R3)/R1 - V1 × R3/R1

Question 35

What is the equation to calculate the output voltage of a differential amplifier when R1 = R2 = R3 = R4

Answer 35

Vout = V2 × R4/(R2 + R4) × (R1 + R3)/R1 - V1 × R3/R1 Vout = V2 × 0.5 × 2 - V1 × 1 Vout = V2 - V1

Question 36

What is the equation to calculate the output voltage of a differential amplifier when R1 = R2 and R3 = R4

Answer 36

Vout = R3/R1 × (V2 - V1)