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Cheap IC versions of operational amplifiers are readily available making their use. popular in any analog circuit, The cheap models operate from DC to about 20 kHz while the high performance. models operate up to 50 MHz, A popular device is the 741 op amp which drops off 6 dB octave above 5 Hz. Op amps are usually available as an IC in an 8 pin dual in line package DIP. Some op amp ICs have more than one op amp on the same chip. Before proceeding we define a few terms, linear amplifier. the output is directly proportional to the amplitude of input signal. open loop gain A, the voltage gain without feedback 105. closed loop gain G, the voltage gain with negative feedback approximation to H j.

negative feedback, the output is connected to the inverting input forming a feedback loop usually. through a feedback resistor Rf, Open Loop Amplifiers. Figure 1a shows a complete diagram of an operational amplifier A more common. version of the diagram is shown in figure 1b where missing parts are assumed to exist. The inverting input means that the output signal will be 180o out of phase with the. input applied to this terminal On the diagram 15V DC and 15V DC is. typically but not necessarily 15V The positive and negative voltages are. necessary to allow the amplification of both positive and negative signals without. special biasing, Figure 1 a Complete diagram of an operational amplifier and b common diagram of an. operational amplifier, For a linear amplifier cf a differential amplifier the open loop gain is. v out A j v i v, The open loop gain can be approximated by the transfer function.

where Ao is the DC open loop gain and Hlow is the transfer function of a passive low. pass filter We can write, A j where Ao 105 and fo 5 Hz. Two conditions must be satisfied for linear operation. 1 The input voltage must operate within the bias voltages. Vcc A o v i v Vcc A o, 2 For no clipping the output voltage swing must be restricted to. Vcc v out Vcc, Ideal Amplifier Approximation, The following are properties of an ideal amplifier which to a good approximation are. obeyed by an operational amplifier, 1 large forward transfer function. 2 virtually nonexistent reverse transfer function, 3 large input impedance Zin any signal can be supplied to the op amp.

without loading problems, 4 small output impedance Zout 0 the power supplied by the op amp is not. 5 wide bandwidth and, 6 infinite gain A, If these approximations are followed two rules can be used to analyze op amp circuits. The input currents Ii and I are zero Ii I 0 Zin, The voltages Vi and V are equal Vi V A. To apply these rules requires negative feedback, Feedback is used to control and stabilize the amplifier gain The open loop gain is too large. to be useful since noise will causes the circuit to clip Stabilization is obtained by feeding. the output back into the input closed negative feedback loop In this way the closed loop. gain does not depend on the amplifier characteristics. Non inverting Amplifiers, Figure 2 shows a non inverting amplifier sometimes referred to as a.

voltage follower, Figure 2 Non inverting unity, gain amplifier. Applying our rules to this circuit we have, Vi V Vin Vout. Ii I 0 Rin, The amplifier gives a unit closed loop gain G j 1 and does not change the sign of. the input signal no phase change, This configuration is often used to buffer the input to an amplifier since the input. resistance is high there is unit gain and, no inversion The buffer amplifier is also used.

to isolate a signal source from a load, Often a feedback resistor is used as shown in figure 3. Figure 3 Non inverting, amplifier with feedback, For this circuit Vi V V in V. R I R f out, Vout R RI R, The gain is i 1 F, with G j 1. Inverting Amplifiers, An inverting amplifier is shown in figure 4. Analysis of the circuit gives Figure 4 Inverting amplifier. Vin V V Vout, Since Vi V 0 V is at virtual ground Vin Vout.

The gain is G j, The output is inverted with respect to the input signal. A sketch of the frequency, response of the inverting and. non inverting amplifiers are, shown in figure, The input impedance of the inverting. amplifier is Rin Vin I, Since Vin IRI we have Rin RI. A better circuit for approximating an ideal, inverting amplifier is shown in figure.

The extra resistor is a current, bias compensation resistor It. reduces the current bias by, eliminating non zero current at Inverting amplifier with bias. the inputs compensation, Mathematical Operations, Current Summing Amplifier. Consider the current to voltage converter shown in figure Applying our ideal amplifier. rules gives, Vi V 0 0 V out iRF, Therefore Vout iRF and the circuit. acts as a current to voltage converter, Figure shows several current sources driving the.

negative input of an inverting amplifier, Summing the current V1 V2 V3 Vout. into the node gives R1 R2 R 3 RF, Current summing amplifier. If R1 R2 R3 R the output voltage is proportional to the RF. Vout V1 V2 V3, sum of the input voltages R, For only one input and a RF R. Vout Vin F Vref, constant reference voltage RI RR, where the second term represents an offset voltage This provides a convenient method for. obtaining an output signal with any required voltage offset. Differentiation Circuit, To obtain a differentiation circuit we replace the input resistor of the.

inverting amplifier with a capacitor as shown in figure. The frequency response is, shown in figure, Replacing RI with Zc 1 j C in the voltage. gain gives Vout G j Vin Vin j RCVin RC in, Integration Circuit. Integration is obtained by reversing the resistor and the capacitor as shown in figure. The capacitor is now in the feedback loop, The frequency response is shown. Analysis gives, Vout Z 1 1, We can combine the above inverting. summing offset differentiation and, integration circuits to build an analog.

computer that can solve differential, equations However today the. differentiators and integrators are mainly, used to condition signals. Active Filters, Filters often contain embedded amplifiers. between passive filter stages as shown in, Figure 13 Buffer amplifier as part of active filter. These filters have a limited performance since the. poles are still real and hence the knees are not sharp. For example a three stage high pass filter with buffer. amplifiers has a transfer function, j c j c j c j c 3.

1 j c 1 j c 1 j c 1 j c 3, and only drops 18 db octave. For complex poles we must use either integrators or. differentiators Consider figure 14, Figure 14 Active filter with complex poles. The closed loop gain is, Z RC R j C R, RI R R 1 j C RI 1 j RC. By exchanging the input resistor for a capacitor we can change between a low pass and. high pass filter, General Feedback Elements, The feedback elements in an operation amplifier design can be more complicated. than a simple resistor and capacitor An interesting feedback element is the analog. multiplier as defined in figure 15, Figure 15 Five terminal network that performs the multiplication operation on two voltage.

The multiplier circuit itself can be thought of as another op amp with a. feedback resistor whose value is determined by a second input voltage. Multiplication circuits with the ability to handle input voltages of either sign. four quadrant multipliers are available as integrated circuits and have a. number of direct uses as multipliers But when used in a feedback loop. around an operational amplifier other useful functional forms result. Operational Amplifiers The operational amplifier op amp was designed to perform mathematical operations Although now superseded by the digital computer op amps are a common feature of modern analog electronics The op amp is constructed from several transistor stages which commonly