Electrical Circuits II (ECE233b)

Transcription

1 Electrical ircuits II (EE33b) ariablefrequency Network Performance (Part 3) Anestis Dounavis The University of Western Ontario Faculty of Engineering Science

2 Scaling Often the values of circuit parameters vary by orders of magnitudes For example: esistors units M 6 apacitors units pf Inductors units nh 9 Time units ns 9 Frequency units GHz 9 Since computers are finite precision machines, scaling circuit parameters can result in numerically more accurate results. In addition, scaling can sometimes make the results more presentable. There are two ways to scale circuit parameters an scale: Magnitude (or Impedance) scaling Frequency scaling

3 Magnitude Scaling Note magnitude scaling does not affect the frequency response ets verify for series circuit M M K K Q K K Q M M Magnitude Scaling K M K M K M

4 Frequency Scaling Note resistors are frequency independent and are unaffected by this scaling The new inductor and capacitor values must have the same impedance at the scale frequency as the original circuit and must satisfy: j j j j where KF and K F is the frequency scaling factor Frequency Scaling K F K F Frequency independent

5 Note that frequency scaling affects the resonant frequency and bandwidth but not the Q. Frequency Scaling F F F K K K Q /K K Q M M (BW) K Q W B F ets verify for series circuit

6 Example 4 An network has the following parameters values: =, = H and =F. Determine the values of the circuit elements if the circuit is magnitude scaled by a factor of and frequency scaled by factor of.

7 Filter Networks Two types: PASSIE and ATIE circuits Passive Filters circuits composed of passive elements Types of Filters. ow pass filters: allows low frequencies to pass and rejects high frequencies. High pass filters: allows high frequencies to pass and rejects low frequencies 3. Band pass filters: allows some particular band of frequencies to pass and rejects all frequencies outside the range 4. Band reject filters: rejects some particular band of frequencies and allows all other frequencies to pass

8 ow Pass Filters Ideal haracteristic of ow Pass Filter Magnitude Simple ow Pass Filter G (s) I (s) ( s) j I Magnitude Actual characteristic o resonant frequency break frequency half power frequency

9 ow Pass Filters G (s) I j Bode plot approximation Actual response I db db M( ) / 45 9 ( ) tan

10 High Pass Filter Ideal haracteristic of High Pass Filter Magnitude Simple High Pass Filter G (s) I ( s) j j Magnitude I o Actual characteristic

11 High Pass Filters G (s) I j j Bode plot approximation Actual response db db M() I o / 9 45 ( ) 9 tan

12 Band Pass Filter Ideal haracteristic of Band Pass Filter Magnitude O HI Simple Band Pass Filter G (s) I s (s) I O j ( )

13 Band Pass Filter G (j ) Magnitude I M( ) j ( ) ( ) ( ) I O Actual characteristic O HI

14 Band Pass Filter Magnitude Actual characteristic M( ) ( ) ( ) O HI The center frequency ower cut off frequency rad/s Upper cut off frequency O (/) (/) 4 O (/) (/) 4 Bandwidth BW HI O Q

15 Band eject Filter (Notch Filter) Ideal haracteristic of Band eject Filter Magnitude O Simple eject Pass Filter G (s) I s ( s) s ( s) j ( ) j Magnitude ( ) HI I O Actual characteristic O HI

16 Example 5 Given the following circuit parameter values: =59mH, =59mF and =W. Demonstrate that this circuit can be used to produce a lowpass, highpass, or bandpass filter. I =

17 Active Filters Drawbacks of Passive Filters. Inability to generate a network with a gain greater than one since passive elements cannot add energy to signals. Inductors are generally expensive and occupy to much space Advantages of Active Filters. Active Filters are able to add energy to signals. an construct inductors using resistors, capacitors and operational amplifiers (Opamps).

18 Active filters Inverting operational amplifier I I Z Z Z Z O O Noninverting operational amplifier I I Z Z Z I Z ( ) I Z O O Filter characteristics are determined by the choice of Z and Z.

19 Example 6 Find the voltage gain o/ I for the following circuit Example 7 (Difference Amplifier) I O Find the voltage gain o/ I for the following circuit I 3 O

20 Example 8 Find the input impedance for the following circuit Z in

21 Inductor eplacement Antoniou Inductance ircuit I 3 4 Z in Zin s 34 / s I / where 3 4

22 Example 9 Find the transfer function o/ I for the circuit shown below and state what type of filter this transfer function represents O I 3 4 5

23 Example The network shown is a circuit model for a single stage tuned transistor amplifier. Find the transfer function o/ A, and the value of so that the center frequency is 9. MHz. A x.4x =5k =H o

24 Example Design db attenuation at.5 KHz for the following two circuits I a) Single pole low pass filter I b) Twostage buffered low pass filter