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ANALOG ELECTRONICS II FREQUENCY RESPONSE 1 Frequency Response Frequency response refers to how voltage gain varies as frequency changes AC amplifier – gain decreases when input frequency too low or too high DC amplifier – gain falls off at higher frequency Usually use dB to describe the decrease in voltage gain Bode plot – to graph the response of an amplifier 2 Frequency Response of DC amplifier Aol (dB) 3 Open-Loop vs Closed-Loop 4 High-frequency op-amp equivalent circuit V1 + Vid Ro Ri Vout + V2 - AVid C Figure 1: High-frequency model of an op-amp with single break frequency 5 Frequency Response What causes the gain of an op-amp to roll off after a certain frequency is reached? Note: roll off is the rate of decreases in voltage gain with frequency. For each ten times reduction in frequency below fc, there is a 20 dB reduction in voltage gain. Ans: Capacitive component Recall from basic theory: Read Floyd page 493, effect of coupling capacitor 1 XC 2fC Reactance varies inversely with frequency Reactance decreases frequency increases 6 Frequency Response Two major sources are responsible for capacitive effects: Physical characteristics of semiconductor devices The internal construction These two capacitances effect causes the gain of opamp to decrease as the frequency increases Internal transistor capacitances Recall from basic concept: Read Floyd page 494-495 7 Open-loop Frequency response Refer to figure 1 Since Thus, Vout j 1 j Vout and jX C AVid Ro jX C X C 1 2fC AVid 1 j 2fC AVid Ro 1 j 2fC 1 j 2fRoC Hence the openloop voltage gain is Vout Aol ( f ) Vid A Aol ( f ) 1 j 2fRo C 8 Open-loop Frequency response Let f o 1 2RoC then A Aol ( f ) 1 j f fo Where Aol(f) = open-loop gain as a function of frequency A = gain of the op-amp at 0 Hz (dc) f = operating frequency (Hz) fo = break frequency of the op-amp (Hz) Aol ( f ) A 1 f fo 2 f ( f ) tan fo Open-loop gain magnitude 1 Phase angle 9 Closed-loop frequency response Frequency bandwidth is measured at the point where gain falls to 0.707 of maximum signal – The -3dB bandwidth Open loop configurations are extremely bandwidth limited Closed loop configuration significantly increases an opamp’s bandwidth 10 Circuit stability A system is said to be stable if its output reaches a fixed value in a finite time. To test the stability of the systems : Analytical method – Routh-Hurwitz criteria Graphical method – Bode plots How to determine stability? Method 1 Determine the phase angle when the (Aol)(B) is 0 dB or 1. If the phase angle is > -180º ----- stable Method 2 Determine the (Aol)(B) when the phase angle is - 180º. If magnitude is –ve dB --- stable 11 Closed-loop system Vin + Aol(f) Vo - Vf B A typical closed-loop system (noninverting amplifier) Vout Aol Acl Vin 1 Aol B where B = gain of a feedback circuit 12