Lecture VIII Operational Amplifiers DMT 231/3 Electronic II

Op-amp symbols and packages. Figure 1

Basic op-amp representations. Figure 2 IDEAL OP-AMP  infinite voltage gain  infinite bandwidth  infinite input impedance  zero output impedance PRACTICAL OP-AMP  very high voltage gain  very high input impedance  very low output impedance

Basic internal arrangement of an op-amp. Figure 3 Input stage for the op-amp  Provides amplification of the difference voltage between the two inputs  Provides additional gain Output stage

Figure 6 Single-ended input mode. In DIFFERENTIAL MODE either one signal is applied to an input with the other input grounded OR two opposite-polarity signals are applied to the inputs If signal voltage is applied to the inverting input: an inverted, amplified voltage appears at the output. If signal voltage is applied to the non-inverting input: a non- inverted, amplified voltage appears at the output.

Differential input mode. Figure 7 Two opposite-polarity (out of phase) signals are applied to the inputs  Amplified difference between the inputs appears on the output.

Common-mode operation. Figure 8 Two signal voltages of the same phase, frequency and amplitude are applied to both inputs  Resulting in a zero output voltage = COMMON-MODE REJECTION  Unwanted signal will not appear on the output & distort the desired signal

Common-Mode Rejection Ratio The measure of an amplifier’s ability to reject common-mode signals  Desired signals can appear on only one input OR with opposite polarities on both input lines.  Unwanted signals (noise) appearing with the same polarity on both input lines are essentially cancelled by the op-amp & do not appear on the output.

Common-Mode Rejection Ratio  The HIGHER the open-loop gain with respect to the common mode gain, the BETTER the performance of the op-amp in terms of rejection of common-mode signals. Equation 1 Equation 2

Open-Loop Voltage Gain, A ol  INTERNAL voltage gain & represents the ratio of output voltage to input voltage when THERE NO EXTERNAL components. Maximum Output Voltage Swing, V o(p-p)  Quiscent output voltage: with no input signal, output is ideally 0V  V o(p-p) : varies with the load connected to the op-amp & increases directly with load resistance.

Input bias current is the average of the two op-amp input currents. Figure 9 Equation 3

Op-amp input impedance. Figure 10 Total resistance between the inverting & non- inverting inputs  Measured by determining the change in bias current for a given change in differential input voltage resistance between each input & ground  Measured by determining the change in bias current for a given change in common-mode input voltage

Op-amp output impedance. Figure 12 Resistance viewed from the output terminal of the op-amp

Slew-rate: the maximum rate of change of the output in response to a step input voltage  dependent upon the high-frequency response of the amplifier stages within the op-amp. Figure 13 Equation 4

Figure 14 Exercise 1: Determine the slew rate.

Negative Feedback: process whereby a portion of the output voltage of an amplifier is returned to the input with a phase angle opposes the input signal. Figure 15

Without negative feedback, a small input voltage drives the op- amp to its output limits and it becomes nonlinear. Figure 16

Closed-Loop Voltage Gain, A cl  Voltage gain of an op-amp with external feedback  Determined by the external component values & can be precisely controlled by them.

Non-inverting amplifier. Figure 17

Differential input, V in - V f. Figure 18

Equation 5 Equation 6 Equation 7 Equation 8 Equation 9 Equation 10

Figure 19 Exercise 2: Determine the closed-loop voltage gain of the amplifier

Op-amp voltage-follower: special case of the non-inverting amplifier where all of the output voltage is fed back to the inverting input by a straight connection Figure 20 Equation 11

Inverting amplifier. Figure 21

Virtual ground concept and closed-loop voltage gain development for the inverting amplifier. Figure 22

Equation 12 Equation 13 Equation 14 Equation 15 Equation 16

Figure 23 Exercise 3: Determine the value of R f required to produce a closed-loop voltage gain of -100

Figure 24 Input Impedance of Non-Inverting Amplifier

Equation 17 Equation 18 Equation 19 Equation 20 Equation 21 Equation 22 Equation 23 Equation 24

Figure 25 Output Impedance of Non-Inverting Amplifier

Equation 25 Equation 26 Equation 27 Equation 28 Equation 29 Equation 30 Equation 31 Equation 32 Equation 33

Figure 26 Exercise 4: Determine the input & output impendances given that Z in = 2 MΏ, Z out = 75 Ώ, Aol =

Figure 26 Exercise 5: Find the closed-loop voltage gain

Equation 34 Equation 35 Voltage Follower Impedances

Inverting amplifier. Figure 27

Figure 28

Equation 36 Equation 37

Figure 29 Exercise 6: Determine the input & output impendances given that Z in = 4 MΏ, Z out = 50 Ώ, A ol =

Figure 29 Exercise 7: Determine the closed-loop voltage gain

Ideal plot of open-loop voltage gain versus frequency for a typical op-amp. The frequency scale is logarithmic. Figure 38

Closed-loop gain compared to open-loop gain. Figure 44

Effect of Negative Feedback on Bandwidth Equation 38 Equation 39 Equation 40 Equation 41

Figure 45 Exercise 8: Determine the bandwidth of each amplifiers given that the open-loop gain is 100 dB & unity-gain bandwidth,f T of 3 MHz