Operational Amplifiers 132022 Costas Foudas Imperial College Rm

Operational Amplifiers 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 1

The Operational Amplifier • The Op. Amp uses a High and a Low voltage supply (e. g. +15 V and – 15 V. The output of the Op. Amp cannot exceed these values usually referred as ‘rail voltages’ • Vout= A * (V+-V-) Typically: A >> The output goes to the positive rail If V+ > Vand it goes to the negative rail if V+ < V • The Input impedance is large (not much current flows) • The Output impedance is small (current can flow) 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 2

Negative Feedback and the Operational Amplifier Vin +V + -A -V G*Vout G Vout So: Vout = A (Vin - G*Vout) Vout(1 + A*G) = A Vin Vout = [A/ (1+ A*G)]* Vin So the GAIN = [A/ (1+ A*G)] is stable if the feedback is negative as shown. If the feedback is negative: V+ = Vin = Vout * G V- = G * Vout The Op. Amp will try to make its inputs equal 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 3

Operational Amplifier Rules Vin + - +V A Vout -V G*Vout G You can analyze all Op. Amp circuits using the following rules: • The output attempts to do whatever it takes to make the voltage difference of the inputs zero (under negative feedback) (2) Inputs draw no current 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 4

Feedback in General In General the feedback could be positive or negative: So: Vout = A (Vin + G*Vout) Vx Vy X Vout(1 - A*G) = A Vin A Vout = [A/ (1 - A*G)]* Vin where G is either G positive or negative G*Vy G < 0 GAIN = [A/ (1 + A * |G|)] and the output is stable (neg. feedback) IF G > 0 GAIN = [A/ (1 - A * |G|)] the output is unstable and the system oscillates IF 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 5

The 741 Operational Amplifier Do not forget to give the Op. Amp BOTH positive and negative power. Some Op. Amp will operate also Between 0 and +V You can find a good collection of Op. Amps in http: //www. analogdevices. com/ 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 6

The Voltage Follower Negative Feedback : Useful for connecting a source that cannot drive much current to a load that needs current (to maintain a voltage level). Alternatively: to connect a high impedance source to a low impedance load without voltage degradation. Exercise I : Show that Vout = Vin 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 7

Exercise II : The Voltage Follower 1 Mohm 10 Volt Source can drive a 750 Ohm Load. Try doing this without an active device like an Op. Amp or some transistor l Notice that the Op. Amp Output cannot rise instantly. The Slew rate (Volts/ sec) indicates how fast is the Op. Amp. l 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 8

The Inverting Amplifier I Negative Feedback : Exercise III : Show that Vout = - (R 2/R 1)*Vin 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 9

Exercise IIIa : The Inverting Amplifier The output is twice the input as expected l The output cannot be larger than the upper rail voltage or smaller that the lower rail voltage. If that happens the output voltage clips and stays equal to the rail voltage l 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 10

Exercise IIIb : Frequency Responce Internal capacitance reduces the output voltage at high frequencies l High Frequencies are suppressed !!!! l The Op. Amp Acts like a low pass filter ! l 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 11

Exercise IV: The Non-inverting Amplifier Negative Feedback : Exercise : Show that Vout = (1+R 2/R 1)*Vin 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 12

Summing Junction with an Op. Amp Summing Amplifier with Negative Feedback : Exercise V : Show that Vout = - (V 1+V 2+V 3) 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 13

Digital to Analog Converter (DAC) Making a digital to analog converter : How does this work ? ? ? 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 14

Differential Amplifier Common mode noise at the input cancels out l Signals are usually transmitted at long distances differentially in order to cancel any pick-up noise. l 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 15

Integrators and Differentiators 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 16

Current to Voltage Converters 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 17

Positive Feedback- Oscillators 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 18

Voltage Controlled Oscillator I Op. Amp in Negative Feedback; Capacitor is charging at constant current. 1/3/2022 Schmitt Trigger Costas Foudas, Imperial College, Rm: 508, x 47590 19

Voltage Controlled Oscillator II 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 20

Voltage Controlled Oscillator III Lower trace is the input voltage l Upper trace is the VCO modulated output l 1/3/2022 Costas Foudas, Imperial College, Rm: 508, x 47590 21