Understanding Thevenin & Norton Circuits: Impedance Matching & Op-Amps, Study notes of Physics

Download Understanding Thevenin & Norton Circuits: Impedance Matching & Op-Amps and more Study notes Physics in PDF only on Docsity! Electronics 1: Lecture 3 • Thevenin & Norton Equivalent Circuits • Impedance Matching • Operational Amplifier Black Box Example: Real Batteries… linear model: output (or source) resistance Rs Batteries are good voltage sources, but still: More current drawn voltage goes down Do not try to measure this resistance with your -meter… It may damage your meter! voltage U = Uemf -IRs Rs Uemf Thevenin/Norton Example: Norton: INeq = short-circuit current RNeq = independent sources 0 RNeq = Req = RTeq UTeq = INeqReq Thevenin: UTeq = open-circuit voltage RTeq = independent sources 0 2A 12V 4 8 8 5 Step 1: Sources Zero 2A 12V 4 8 8 5X X = 5 parallel to (8+4+8) = 5 20 / (5+20) = 4 Remark: Sources themselves ideal again… Remember: voltage sources short circuit current sources open circuit Req Step 2 (Thevenin): Open-Circuit 2A 12V 4 8 8 5 Node analysis: 2A i2 i3 U U = i25 = 5 4/5A = 4 V = UTeq u1 } { i25 = U 2A = i2 + i3 12V + 4 i3 = u1 (8+5+8) i2 = u1 12V + 4 i3 = (8+5+8) i2 2A - i2 = i3 20V=25 i2 i2 = 4/5 A Transferring Power to a Load Connect a load … and get a voltage divider: I = UTeq/(RL + RTeq) Maximum power transfer: RL? (RL+RTeq) – 2RL = 0 RTeq = RL impedance matching RTeq UTeq RL uL = RL RL + RTeq UTeq PL = IuL = UTeq 2 RL +RTeq( ) 2 RL PL RL = UTeq 2 (RL +RTeq) 2 2RL UTeq 2 (RL +RTeq) 3 = 0 P L R L = 0 Chaining Things together: power transfer impedance matching !!! Mixer o u tp u tin p u t Synthesizer (Source) o u tp u t Amplifier o u tp u tin p u t Speaker (Load)in p u t Feedback Def.: Compare real output with desired output apply correction! Example: voltage amplifier desired output: Vout = a Vin feedback: VFB = Vout / a ideal amplifier: VFB – Vin = 0 real amplifier: VFB – Vin = V positive feedback: Vin Vin + V V negative feedback: Vin Vin – V V 0 ( >0) Infinite Gain: What’s the Idea? - positive feedback two stable output states: +/-Vmax (saturation) - negative feedback one stable output state: Uin = 0V for negative feedback: Summing Point Constraint or Virtual Equality: Differential input voltage Uin = 0 !!! (to be used in circuit analysis!) Real Op-Amp Parameters: (±) 5-24 Vsupply voltage VEE,VCC 010-100 output resistance Rout 106-1013 input resistance Rin 105-108open loop gain A idealtypicalParameter equivalent circuit +VCC -VEE Voltage Follower: input voltage = output voltage !!! input current = 0 !!! output resistance very small it acts as a buffer isolates the load from the source Is it useful ??? Uout Uin Finite Gain: Non-Inverting Amplifier v2 Vo V1 R2 R1 ideal: real (i.e. limited open-loop gain A): real: bottom line: R1=98k , R2 = 2k Vo = A(V1-v2) v2 = VoR2/(R1+R2) Vo = A(V1-VoR2/(R1+R2)) Vo(1/A + R2/(R1+R2)) = V1 Gid=50; A=10 5 Gre=49.9999 A=8x104 Gre=49.969 V o = V 1 1+ R 1 R 2 V o = V 1 1 A + R 2 R 1 +R 2 Op-Amps: Think Op-Amp, think: 1.) 2.) 3.) 4.) Feedback neg. feedback Virtual Equality Input Impedance = (i.e. iin = 0!) Output Impedance = 0 (i.e. iout = whatever needed!) Another way to look: RFRS R1 R2 RFRS R1 R2 Non-Inverting Inverting Vo = -V1 R2/R1 Input Impedance? V o = V 1 1+ R 1 R 2