1. Everything You Ever Wanted to Know About Filters*
Class 1: Analog Filters I: Resonant Circuits and Passive Filters
June 8, 2015
Charles J. Lord, PE President, Consultant, Trainer Blue Ridge Advanced Design and Automation
* But were afraid to ask

2. This Week’s Agenda
6/8 Analog Filters I: Resonant Circuits and Passive Filters 6/9 Analog Filters II: Active Filters 6/10 Digital Filters I: Sampling and the Z-Transform 6/11 Digital Filters II: Infinite impulse response filters 6/12 Digital Filters III: Finite impulse response filters and Conclusion

3. This Week’s Agenda
6/8 Analog Filters I: Resonant Circuits and Passive Filters 6/9 Analog Filters II: Active Filters 6/10 Digital Filters I: Sampling and the Z-Transform 6/11 Digital Filters II: Infinite impulse response filters 6/12 Digital Filters III: Finite impulse response filters and Conclusion

4. Resonance Everywhere! FILTERS!
Unless we are at steady-state DC, we are affected by resonant circuits
Even getting to steady state can be of concern
There is always noise!
Remembering these concepts can be helpful
AND – we can use resonance to our advantage:
FILTERS!

5. Transmission Lines

6. Resource Material
This class builds on my class from last semester, “Analog Design for the Digital World”
The following URLs are Day 1 through Day 5

7. Series Resonance V = VM 0 R L C V _ I+ C V _ I
The input impedance is given by:
The magnitude of the circuit current is;

8. Resonance occurs when
At resonance we designate w as wo and write;
This is an important equation to remember. It applies to both series
And parallel resonant circuits.

9. The magnitude of the current response for the series resonance circuit
is as shown below.
|I|
Half power point w1 wo w2 w
Bandwidth:
BW = wBW = w2 – w1

10. The peak power delivered to the circuit is;
The so-called half-power is given when .
We find the frequencies, w1 and w2, at which this half-power
occurs by using;

11. After some insightful algebra one will find two frequencies at which
the previous equation is satisfied, they are:
and
The two half-power frequencies are related to the resonant frequency by

12. The bandwidth of the series resonant circuit is given by;
We define the Q (quality factor) of the circuit as;
Using Q, we can write the bandwidth as;
These are all important relationships.

13. An Observation: If Q > 10, one can safely use the approximation;
These are useful approximations.

14. Remember!
A capacitor isn’t always Or
But can also be:

15. Remember!
An Inductor isn’t always
But can be
Or even

16. Parallel Resonance
What this means is that for all the equations we have
derived for the parallel resonant circuit, we can use
for the series resonant circuit provided we make
the substitutions:

17. Parallel Resonance
Parallel Resonance
Series Resonance

18. Filters
Now that we know something about bandpass (and conversely bandstop), let’s look at some others:
Lowpass:

19. Taking out the Inductor

20. High Pass
Thus a simple, first-order passive high-pass filter becomes

21. Designing and Modeling
A good toolbox is always needed! The program SPICE (Simulation Program with Integrated Circuit Emphasis) has been around since 1973 – I first used it in 1978
Now, variations of SPICE are graphical – tied into schematic entry software.
My examples are using the free version of ORCAD – for more information see Day 5 of the previous class:

22. Set Up a Transient Simulation

23. Resultant

24. But…
The passive filters we looked at are not isolated – they are affected by the impedances of the circuitry that the input and output are attached to
If this impedance is matched, or is orders of magnitude greater (at output) or less (at input), they might be ignored
If only we could add a high impedance input and a low impedance output (and perhaps gain!)
Tune in tomorrow!

25. This Week’s Agenda
6/8 Analog Filters I: Resonant Circuits and Passive Filters 6/9 Analog Filters II: Active Filters 6/10 Digital Filters I: Sampling and the Z-Transform 6/11 Digital Filters II: Infinite impulse response filters 6/12 Digital Filters III: Finite impulse response filters and Conclusion

26. Please stick around as I answer your questions!
Please give me a moment to scroll back through the chat window to find your questions
I will stay on chat as long as it takes to answer!
I am available to answer simple questions or to consult (or offer in-house training for your company)