Feedback (continued) From Chapter 12 – Section 12.6 K Feedback Lecture 1 Feedback & Op-Amps Go Together Ideal Op-Amp has A (infinite) Rin (infinite) Rout 0 vout R1 1 vin R2 Op-Amps make the use of feedback easy! Feedback Lecture 2 Analysis Methodology 1.Identify the forward network 2.Identify the feedback network 3.Break the feedback network 4.Calculate the open-loop parameters 5.Determine the feedback factor 6.Calculate the closed-loop parameters Feedback Lecture 3 Breaking a Loop Loading input & output nodes must be accounted for. How do we Terminate? • The correct way to break a loop is to do it so that the loop does not know it has been broken. The feedback network is duplicated at both input and output – this allows the correct loading to be placed at both the input and output. Feedback Lecture 4 Rules for Breaking the Loop of Amplifier Types Sense-Return Voltage-Voltage Voltage-Current Current-Current Current-Voltage Feedback network K is duplicated at both the input and output. Feedback Lecture 5 Example: Voltage-Voltage Feedback Input of Network K sees zero impedance Output of Network K sees large impedance Return Sense • Ideally, the input of the feedback network sees zero impedance (Zout of an ideal voltage source), the return replicate needs to be grounded. Also, the output of the feedback network sees an infinite impedance (Zin of an ideal voltage sensor), the sense replicate needs to be open. • Analogous arguments apply to the three other types. Feedback Lecture 6 Example: Voltage-Voltage Feedback Input of Network K sees zero impedance Output of Network K sees large impedance Return Sense • As step 4 we can calculate the open-loop parameters with the forward network being correctly loaded from the feedback network (but with the feedback network broken and not functional). • Next, we go to step 5 which is to calculate the feedback factor and then on to step 6 to calculate closed-loop parameters with the feedback network accounted for. Feedback Lecture 7 Calculation of Feedback Factor Voltage-Voltage Current-Current Feedback Lecture Voltage-Current Current-Voltage 8 Example Feedback Network CG stage Av ,open gm 1 RD Rin ,open 1 gm 1 Rout ,open RD R1 R2 Open-loop gain calculated with correct loading R1 R2 Feedback Lecture 9 Determining the Feedback factor K V2 R2 /( R1 R2 ) V1 and Av ,open gm 1 RD ( R1 R2 ) R2 Therefore, KAv ,open gm 1 RD ( R1 R2 ) R1 R2 To get closed-loop gain, Av ,closed Av ,open /(1 KAv ,open ) Feedback Lecture 10 Closed-Loop Parameters K V2 R2 /( R1 R2 ) V1 and Av ,open gm 1 RD ( R1 R2 ) gm 1 RD ( R1 R2 ) Av ,closed R2 1 gm 1 RD ( R1 R2 ) R1 R2 R2 (1 KAv ,open ) 1 gm 1 RD ( R1 R2 ) R1 R2 R2 1 g ( R ( R R )) m1 D 1 2 R R 1 2 ( RD ( R1 R2 )) /(1 KAv ,open ) R2 1 g ( R ( R R )) m1 D 1 2 R1 R2 Rin ,closed Rin ,open (1 KAv ,open ) Rout ,closed Rout ,closed 1 gm 1 Feedback Lecture 11 Another Example: Transimpedance Amplifier Voltage Sense – Current Return Feedback Lecture 12 Transimpedance Amplifier (continued) AZ , open Vout RF RD 1 gm 2 RD 2 RF 1 I in open RF gm 1 1 K , RF so RZ ,in , open 1 RF gm 1 1 KA Z , open 1 RF RD 1 1 gm 2 RD 2 RF 1 RF RF g M 1 RZ , out , open RD 2 RF Feedback Lecture 13 Transimpedance Amplifier (continued) Vout I in open Vout AZ ,closed I in closed Vout 1 K I in open RF RD1 g ( R R m2 D2 F RF gm11 AZ ,closed 1 RF RD1 1 g ( R R m2 D2 F RF RF gm11 RZ , in ,closed RZ , out ,closed Vout RZ ,in , open /(1 K ) I in open Vout RZ ,out ,open /(1 K ) I in open Feedback Lecture 14 Another application of feedback: Electronic Oscillator Feedback Lecture 15 RC Phase Shift Feedback oscillator BJT (or FET) Feedback Lecture 16 RC High Pass Filter Section +60 At 60 each RC section has loss of 0.185 (or -14.7 dB) Feedback Lecture 17 Feedback Network for Oscillator N=3 f osc 1 2 RC 2 N where N = number of RC sections Feedback Lecture 18 Feedback Network & Gain Stage Any inverting gain stage will work here A > 29.2 KA 1 180 o Closed-loop gain Aopen 1 KAopen Oscillation criterion: Barkhausen condition KA 1 and KA 2 n (n 0, 1, 2, 3 ... .) Feedback Lecture 19 6.5 kHz RC Oscillator using an Op-Amp Simple and practical implementation of an RC oscillator Inverting Op-Amp Feedback Lecture 20 RC Oscillator Startup Closed-loop gain Aopen 1 KAopen Initially, loop gain is too large for a steady-state oscillation, so amplitude builds up to until amplitude compression occurs; then loop gain falls until the condition KA = 1 is met. Question: What starts the oscillation to begin? Feedback Lecture 21 Now what? Feedback Lecture 22