Chapter 4 – Operational Amplifiers – Part 2 Mathematical Operations Operational Amplifier Applications

Symbol for Operational Amplifier Block diagram of Operational Amplifier (Op-Am) Conventional circuit symbol for (Op-Am)

The operational amplifier circuit is simplified by a conventional symbol by not showing the ground terminals. The operational amplifier is indicated by a triangle pointing towards the output terminal.

1. Inverting Amplifier The point S is at virtual ground potential. The ratio - Rf/R = A (also gives the gain of the Op-amp). The output voltage vo = (- Rf/R ) vi. If Rf = R, the output voltage vo = -vi. The signal is simply multiplied by -1. Multiplicative factors vary from – 0.1 to -10.

2. Non-inverting Amplifier The operational feedback connection is separated from the signal input voltage. The key point is that point S is not at a virtual ground potential. The important thing is that the voltage difference between S (i.e. V-) and signal input voltage vi (i.e. V+) is kept near zero, (i.e. V-  V+)

The output voltage inverting op-amp, vo = (- Rf/R ) vi. The voltage gain of op-amp = vo /vi (Take absolute value). The gain of op-amp in dB = 20 log (vo /vi ). Stage 1, AV = 1.766 = 4.940 dB Stage 2, AV = 0.455 = -6.848 dB Overall gain = AV1 x AV2 = 1.766 x 0.455 = 0.803 overall gain in dB = 20 log (vo/vi) = 20 log (0.803) = -1.909 dB If AV = 1 = 0 dB Amplifier voltage gain = 0.47 = -6.55 dB

Checkpoint - 1 Find Vo (12V) Find potential at S (2V) Current flowing through R1. Direction of the current flowing through the R1 and R2.

Check point 2: An open-loop voltage gain of an operational amplifier () is 100,000, and the inverting input connected directly to its output terminal. Calculate the output voltage for a noninverting input voltage of +5 volts.

Check point 3: An open-loop voltage gain of an operational amplifier () is 100,000, and the inverting input connected to a voltage divider on its output terminal (so the inverting input receives exactly one-half the output voltage). Calculate the output voltage if the noninverting input voltage is -2.4 volts.

Check point 4: Calculate the overall voltage gain of this amplifier circuit (AV ), both as a ratio and as a figure in units of decibels (dB). Given the resistor values of R1 and R2. Find the current in R2 if Vin = 2V.

Check point 5: Calculate all voltage drops and currents in this circuit, complete with arrows for current direction and polarity markings for voltage polarity. Then, calculate the overall voltage gain of this amplifier circuit (AV ), both as a ratio and as a figure in units of decibels (dB). Find the output voltage and overall voltage gain if R2 changed to 27k.

3. The voltage Follower They have stable unity gain. Best frequency bandwidth.

4. Summing Amplifier (or Voltage adder) - vo = vo1 + vo2 + vo3 vo = - (Rf / R1)v1 – (Rf / R2)v2 - (Rf / R3)v3 vo = - Rf (v1/R1 + v2 /R2 + v3 /R3) 1. Many signals can be added in this way. 2. The addition takes place at point S, called the summing point.

5. Difference Operational Amplifier Show that the output signal of the amplifier is vo = (Rf /R ) ( vi – v1). (If Rf = 1.2k, R = 120, v2 = 3 mV, v1 = 1 mV, then vo = ?).

Reactive Elements 1. Integrating Circuit The feed back resistor is replaced by a capacitor. The output voltage is the integration of the input signal. Applications:- (i) Triangle wave generation, (ii) Ramp generation.

-

If the input voltage is a square wave, the output waveform will be triangular. For rectangular or pulse waveform applied at the input, the output waveform will be a sawtooth wave (ramp). The output will be a cosine wave for sine wave input. The output is a paraboloid waveform if the input is a triangular wave. Ramp Generator

Checkpoint 6: In an operational amplifier circuit, the resistance R = 10 k, the capacitance C = 0.1 F, Find the output voltage of integrator amplifier during the time interval of 0 – 1 sec. (i) the input signal Vi = 2 V, (ii) the input signal Vi = (2 + t)V, (iii) the step input voltage is Vi = 0V for t < 0 and switched at t = 0 to 5 V.

2. Differentiating Circuit

Checkpoint - 7: The input to an op-amp differentiator circuit is a sinusoidal voltage of peak value 10μV and frequency of 2 kHz. If the values of differentiating components are given as R = 40 kohm and C =3μF , determine the output voltage.

Operational Amplifier Circuits Connection diagram for the LM741 and LF411 8 pin dual inline packages (DIPs).

offset null connections pins 1 and 5) provide a simple way to balance out the internal variations and zero out the output offset which might be apparent with zero input voltage. connect a trimmer potentiometer between pins 1 and 5. The slider on the potentiometer is connected to the negative power supply. To adjust for zero offset, ground the input resistor and use the offset null potentiometer to set the output voltage precisely to zero.

Absolute Maximum Ratings

Open Loop Characteristics

DC open loop gain is 10000. Supply voltage is  15V. The output saturation occurs at  13.5V. Then, for a linear operation, the input voltage can not exceed 2.7 mV = (+13.5 – (-13.5))/10000. Therefore, the open loop amplifier is not useful for linear operation. The open loop gain is given by the slop of the curve (so Op-amp amplifies between the saturation values of Vo). The slope of the curve is dependent on the frequency of the input voltage while saturation remain constant.

Frequency Dependent Properties Frequency response of open loop gain Op-amp. DC open gain is 108 dB. Open loop bandwidth is 1 MHz. Gain has 4 different slopes.

Closed Loop gain

Schmitt Trigger The Schmitt trigger is a comparator application which switches the output negative when the input passes upward through a positive reference voltage.