1. CHAPTER 12
Filter
Circuits

2. Objectives Describe and Analyze: Filter types: LPF, HPF, BPF, BSF
Passive filters
Active filters
LC tuned amplifiers
Other filter topics
Troubleshooting

3. Introduction
A filter is a circuit designed to separate signals from each other based on their frequency. There are four basic types:
Low-Pass Filter (LPF): passes signals below some frequency
High-Pass Filter (HPF): passes signals above some frequency
Bandpass Filter (BPF): passes signals between two frequencies
Bandstop Filter (BSF): blocks signals between two frequencies

4. Bands are measured to the 3dB points.
Frequency Response
Bands are measured to the 3dB points.

5. Passive RC Filters
All four types of filter can be made with just resistors and capacitors. They are not “high performance”, but they work.

6. RC Filters The frequency f = 1/(2RC) has several names:
Break frequency
Corner frequency
Cutoff frequency
Roll-off frequency
3dB frequency (or -3dB frequency)
0.707 frequency
f0 (“eff-zero”)
fB (“eff-bee”)

7. Bode plot for a”single-stage” LPF (one R and one C)
RC Filters
Bode plot for a”single-stage” LPF (one R and one C)

8. RC LPF Example What is the cutoff frequency for a LPF with
R = 1.59 k and C = 0.01 F ?
Time constant  = RC = (1.59 k)  (0.01 F) = 15.9 s
f0 = 1 / (2 ) = 10 kHz

9. Note that 6 dB /octave is equal to 20 dB /decade.
Bode Plots
Note that 6 dB /octave is equal to 20 dB /decade.

10. Order
The term order used to describe filters tells us how fast the Bode plot rolls off. A first-order filter, such as an RC filter made with one capacitor, has a roll-off of 20 dB/decade, a second-order filter has a roll-off of 40 dB/decade, and so on.
The roll-off is N  20 dB/decade where N is the order of the filter.
You will see the word pole used to mean the same thing: a 1-pole filter is a first-order filter, a 2-pole filter is a second-order filter, and so on.

11. Order
<insert figure here>
The Bode plot says it all.

12. Active Filters
When you make a filter, you want its Bode plot to have a shape appropriate to the application. While a second-order filter can be made with two resistors and two capacitors, its Bode plot will not have a “clean” break-point. That’s where active filters come in.
Active filters use an op-amp together with Rs and Cs. The op-amp’s feedback loop allows you to control the shape of the Bode plot.
Feedback RC filters are often called “Sallen & Key” filters after the two men who first described them in the 1950s. Of course, they used vacuum tubes!

13. Active Filters
(a) is a LPF, (b) is a HPF

14. <insert figure 12-16 here>
Active Filters
<insert figure here>

15. Active Filters

16. Switched Capacitor Filters
Break-point is controlled by clock rate.

17. LC Tuned Amplifier

18. LC Tuned Amps and Q
A tuned circuit amplifier is essentially a bandpass filter with a very narrow pass band. The parameter Q (stands for “Quality”) measures the narrowness of the pass band. How high is high depends on the application, but usually Q = 10 or more is high Q. The width of the pass band is the center frequency divided by Q.
Q = REQ /(2 fo L) where REQ is the equivalent resistance across the parallel LC circuit.

19. Piezoelectric Filters
Piezoelectric crystals and ceramics act like tuned circuits.

20. Troubleshooting Determine the filter type you are working on.
Use an oscilloscope to look at inputs and outputs to check for correct filter response.
If necessary, inject a sine wave and vary the frequency to test the filter response.
Tuned-circuits sometimes “drift”, and may have a small trimmer capacitor to make adjustments.
Active filters either work or the op-amp is dead.
Crystals and ceramics do not drift, but they can crack from rough handling or too much current.