Topology in Circuit Analysis

Transcription

1 Topology in Circuit Analyi Many dierent circuit actually operate the ame Can reduce a circuit to a "graph" Graph only how the branche, not the device Two Circuit are aid to have the ame topology When the graph can be made the ame

2 Example Inverting Op Ampliier For an inverting op am with 1 KΩ CC KΩ EE -15 What i the output or a 0.5 input The voltage gain i: A v o Thu the output i: o Av

3 Analog and Digital Electronic divided into Analog and Digital Analog device: have a continuou range o value All real world ignal are Analog Analog device: example Ampliier: increae/decreae ignal Senor: meaure ome variable eg: light intenity, temperature, air low Tranducer: cover one energy to another orm eg: light to electrical or electrical to heat Analog advantage: Eay repreentation o real world meaurement Wide range o value Can be very at reacting circuit Analog diadvantage: Circuit very tricky to build linear Eg. diicult to keep gain contant in ampliier Thu analog reproduction i inaccurate ery enitive to noie/intererence Eg Ampliication oten inject noie in ignal Thee combine: thu analog reproduction i inaccurate

4 Digital Signal Digital: ignal can only have dicrete value Simplet (commonet) Binary Binary: only two value: 0 (o or low ) or 1 (on or high) Almot all digital device binary at heart Eectively all computer digital thee day Digital advantage: ery accurate i enough digit Noie inenitive, becaue only dicrete value Error ree coping Circuit eay to build Digital diadvantage: Doe not relect continuou real world variable Mut convert rom analog to digital to or computer meaurement Mut convert rom digital to analog or many application

5 Ideal Operational Ampliier (EC 5) Ampliication: increae o a ignal by a contant actor eg. voltage ampliication v A F Ampliication i alo called the gain G Ideal ampliier ideal voltage controlled voltage ource An ideal ampliier doe not aect the input ignal out in

6 Ideal Operational Ampliier "Operational Ampliier": An approximation to ideal ampliier Shorten to "op amp" or common uage Originally ued in Analog computer during ' "Operational Ampliier" rom original unction: Perormance o "mathematical operation" Current device are Integrated Circuit: Full ampliier circuit made at once in a ingle package Mot common o thee called 741 erie In coure treat a a black box: Ignore internal operation: only look at outide behaviour

7 741 Op Amp

8 Ideal Operational Ampliier Op amp act a an ideal ampliier But only over limited input range Have two ignal input: v p and v n (note oten v + and v - ) Signal i applied between them (dierential input) oltage powering device limit operation: Poitive powering voltage CC Negative powering voltage EE Note oten, but not alway EE - CC Text only dicue that condition Symbol imple triangle (power input oten omitted)

9 Ideal Operational Ampliier Behaviour Ideal op amp ha ininite input reitance Thu draw no current rom input ignal Ha 3 area o operation which eect the output v o Linear egion Output linearly related to input v ( v v ) or < A ( v v ) > A ( v v ) o A0 p n EE 0 p n & CC 0 Poitive Saturation Output aturated at poitive power CC o CC or A0 ( vp vn ) CC v > Negative Saturation Output aturated at negative power EE o EE or A0 ( vp vn ) EE v < Note: output can be both poitive and negative Typical gain number A 0 200,000 Ideal op amp, aume gain nearly ininite Thu negligible voltage acro input In coure only conider the linear region p n

10 Feedback and Op Ampliier Adding reitor to op amp can control the gain Gain controlled by Feedback: Feeding output back into input Negative Feedback: output ubtract input ignal Poitive Feedback: output add to input ignal Note poitive eedback generally le table Need to create balance point between output value and op amp v - SP umming point, where output and input ignal um Dierent op amp circuit ue dierent eedback

11 Inverting Op Ampliier Adding reitor to op amp can control the gain Gain controlled by "Feedback": Feeding input back into output Thi circuit give negative gain: Called Inverting op amp SP umming point, where output and input ignal um

12 Inverting Op Ampliier Place a eedback reitor rom op amp output to poitive input The between the etpoint and input in Allow current to low rom input and output to SP Thi circuit give negative gain: Increae ignal but make it negative Called Inverting op amp

13 Inverting Op Ampliier Putting the input into v n give negative gain Output become the oppoite polarity to input p Thu SP a virtual ground In practice ha mall voltage oet 0 I 0 i in in I Ii I in

14 Inverting Op Ampliier Gain equation irtual ground require to revere relative to in out I I out I The ampliication (or gain) i: o v A