Quiz 6 Op-Amp Characteristics

Transcription

1 Lecture Week 11 Quiz 6: Op-Amp Characteristics Complex Numbers and Phasor Domain Review Passive Filters Review Active Filters Complex Impedance and Bode Plots Workshop

2 Quiz 6 Op-Amp Characteristics Please clear desks and turn off phones and put them in back packs You need a pencil, straight edge and calculator 10 minutes Keep eyes on your own paper Follow the same format as for homework

3 Complex/Phasor Impedance Combing frequency dependent and frequency independent passive components introduces the concept of complex impedance. Complex Number: Z = x + iy x = Resistive Part (Frequency independent) iy = Reactance Part (Frequency dependent)

4 Complex Impedance The Phasor Machine will take a time domain function and will give a frequency domain complex function. The resultant function is what we call the impedance. C dv C dt PHASOR MACHINE 1 jwc R PHASOR MACHINE R

5 Capacitor Phasor Domain Proof I is a complex number V is a complex number Assume V = e jwt Then: (1) I = C dv dt (2) C d dt ejwt = jwce jwt (3) I = jwcv (4) V I = 1 jwc

6 Complex Impedance Analysis steps By following these steps you can analyze an RC circuit in the complex/phasor domain 1. Convert every component to its phasor domain representation 2. Find the equivalent impedance by adding individual impedances in series or in parallel 3. Calculate the unknown variable by using ohms law, voltage divider, KCL or KVL

7 Passive Low-Pass Filter Analysis Lets find the equation for for the Low-pass filter circuit using KCL and complex impedance at node Vout. Vin R Vout Vin Z1 = R Vout C Z2 = 1 = I 2 I jwc 2 I 1 I 1 1 jwcr + 1 Complex Impedance Eq. Low- pass filter

8 Passive High-Pass Filter Analysis Lets find the equation for for the High-pass filter circuit using KCL and complex impedance at node Vout. Vin C I 1 I 2 Vout R Vin Z1 = 1 jwc I 1 I 2 Vout Z2 = R = jwcr jwcr + 1 Complex Impedance Eq. High-pass filter

9 Bode Plots and Cutoff frequency A bode plot tell us the magnitude of the RC filter with respect to a range of frequencies. It is a useful graphical tool to determine where the amplitude of the output is starting to drop. The equation to find the frequency at which the amplitude will start to drop is give by the following equation: f c = 1 2πRC (Cutoff frequency)

10 Low-Pass Filter: Bode Plot Vin R Vout C low pass filter = 1 jwcr + 1 Complex Impedance Eq.

11 High-Pass Filter: Bode Plot Vin C R Vout high pass filter = jwcr jwcr + 1 Complex Impedance Eq.

12 Bandpass Filter: Bode Plot = 1 (jwc 2 R 2 + 1) Complex Impedance Eq. jwr 1 C jwr 1 C 1

13 Active Filters An active filter not only gets rid of unwanted frequencies, but it also amplifies those signals that we want A passive filter will only get rid of unwanted frequencies The higher the order of the filter, the more aggressive the roll off will be (the range of frequencies where the amplitude of the signal decreases will be shorter) Active VS Passive

14 Active Filters Cutoff Frequencies An active filter will still amplify signals after the cutoff frequency is reached DO NOT assume that the filter will jump straight to zero after it has hit its cutoff frequency STILL AMPLYFING

15 Making Sense of a Bode Plot Everything above 0 db means amplification or > 0 db means no change or = Everything below 0 db means diminishment or <

16 In-Class Exercise: Active Low-Pass Filter using KCL at node A and complex impedance C Vin R1 I 1 I 2 A R2 Vout = R 2 R 1 1 (jwcr 2 + 1) Complex Impedance Eq. Complex Impedance Eq. Which R contributes to the filtering part, and which contribute to the amplification part?

17 Active High-Pass Filter using KCL at node A and complex impedance. R2 Vin R1 C I 1 A I 2 Vout jwcr 1 = R 2 /R jwr 1 C Complex Impedance Eq.

18 Low-Pass Active Filter: Bode Plot = R 2 R 1 1 (jwr 2 C + 1) Complex Impedance Eq.

19 High-Pass Active Filter: Bode Plot = R 2 R 1 jwcr jwr 1 C Complex Impedance Eq.

20 Band-Pass Active Filter: Bode Plot = R 2 1 jwr 1 C 1 R 1 (jwc 2 R 2 + 1) 1 + jwr 1 C 1 Complex Impedance Eq.

21 COMPLEX IMPEDANCE MODELS FIRST ORDER First Order LOW PASS HIGH PASS PASSIVE = 1 jwcr + 1 = jwcr jwcr + 1 ACTIVE = R 2 R 1 1 (jwr 2 C + 1) = R 2 R 1 jwr 1 C 1 + jwr 1 C SECOND ORDER **Notice the common components for all types of low pass filters and for all types of high pass filters**

22 COMPLEX IMPEDANCE MODELS FIRST ORDER All low pass filters have this expression: = 1 jwcr + 1 SECOND All high ORDER pass filters have this expression: = jwcr jwcr + 1

23 10 minute Break

24 Workshop

25 P1. Find the complex impedance equation for the Active High-Pass Filter using KCL at node A. R2 Vin R1 C A I 2 I 1 Vout

26 What s Next in Week 12? Will introduce LAB Module VII Pressure Sensor LECTURE Quiz #7 Active Filters Review: Active Filters Complex Impedance High order filters Filter Design Please bring laptops to all lectures and labs.

27 Questions?