What are the 3 configurations for OpAmps?

> Non-inverting

> Inverting

> Schmitt Trigger

What are the features of the OpAmp component?

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

> 1 Output

> Gain, Symbol A

What is an important aspect of the inputs?

> They draw no current

> They are 'virtually' shorted together

What can be said about the gain of an amplifier?

Infinite.

Only limited by the power-supply

What is the simplification of an OpAmp?

A voltage controlled ideal voltage source.

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

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

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

What is the configuration of a non inverting amplifier?

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.

What is the equation for a non-inverting amplifier?

Vout = V[+] × (R1 + R2)/R2

What is the concept of negative feedback?

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.

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

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

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

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[+](R1 + R2)/R2

What is the configuration of an inverting amplifier?

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).

What is the equation for the inverting amplifier?

Vout = -(R2/R1)Vin

What is the concept of 'virtual' ground?

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.

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

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

What is the configuration for an inverting schmitt trigger?

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

What is positive feedback?

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

What is the chain of events for positive feedback?

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.

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

The saturation voltage

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

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

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

The schmitt trigger will be at negative saturation.

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

When: Sat+ < Vin ⇒ Sat-

When: Sat- > Vin ⇒ Sat+

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

V+ = VsatR1/R2+R1

V+ = -VsatR1/R2+R1

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

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

How does a non-inverting schmitt trigger work?

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.

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

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

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

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

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

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

What is a Twin-T notch filter?

A band-stop filter

What is the configuration for a Twin-T notch filter

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

Notch frequency f = 1/2πRC

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

R1 < R2 << R

Q = R2/4R1

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

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

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

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

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

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

Vout = V2 × 0.5 × 2 - V1 × 1

Vout = V2 - V1

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

Vout = R3/R1 × (V2 - V1)