1. Everything You Ever Wanted to Know About Filters*
Class 2: Analog Filters II: Active Filters
June 9, 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. Differential Amplifier Model: Basic
Represented by:
A = open-circuit voltage gain
vid = (v+-v-) = differential input signal voltage
Rid = amplifier input resistance
Ro = amplifier output resistance
The signal developed at the amplifier output is in phase with the voltage applied at the + input (non-inverting) terminal and 180° out of phase with that applied at the - input (inverting) terminal.

5. Ideal Operational Amplifier
The “ideal” op amp is a special case of the ideal differential amplifier with infinite gain, infinite Rid and zero Ro .
and
If A is infinite, vid is zero for any finite output voltage.
Infinite input resistance Rid forces input currents i+ and i- to be zero.
The ideal op amp operates with the following assumptions:
It has infinite common-mode rejection, power supply rejection, open-loop bandwidth, output voltage range, output current capability and slew rate
It also has zero output resistance, input-bias currents, input-offset current, and input-offset voltage.

6. The Inverting Amplifier: Configuration
The positive input is grounded.
A “feedback network” composed of resistors R1 and R2 is connected between the inverting input, signal source and amplifier output node, respectively.

7. Inverting Amplifier:Voltage Gain
The negative voltage gain implies that there is a 1800 phase shift between both dc and sinusoidal input and output signals.
The gain magnitude can be greater than 1 if R2 > R1
The gain magnitude can be less than 1 if R1 > R2
The inverting input of the op amp is at ground potential (although it is not connected directly to ground) and is said to be at virtual ground.
But is= i2 and v- = 0 (since vid= v+ - v-= 0)
and

8. Inverting Amplifier: Input and Output Resistances
Rout is found by applying a test current (or voltage) source to the amplifier output and determining the voltage (or current) after turning off all independent sources. Hence, vs = 0
But i1=i2
Since v- = 0, i1=0. Therefore vx = 0 irrespective of the value of ix .

9. Inverting Amplifier: Example
Problem: Design an inverting amplifier
Given Data: Av= 20 dB, Rin = 20kW,
Assumptions: Ideal op amp
Analysis: Input resistance is controlled by R1 and voltage gain is set by R2 / R1.
and Av = -100
A minus sign is added since the amplifier is inverting.

10. Active Filters
Now we can add these structures to the feedback and bias of our opamps from yesterday, with powerful results
Sallen-Key:

11. The Active Low-pass Filter
Use a phasor approach to gain analysis of this inverting amplifier. Let s = jw.
fc is called the high frequency “cutoff” of the low-pass filter.

12. Active Low-pass Filter (continued)
At frequencies below fc (fH in the figure), the amplifier is an inverting amplifier with gain set by the ratio of resistors R2 and R1.
At frequencies above fc, the amplifier response “rolls off” at -20dB/decade.
Notice that cutoff frequency and gain can be independently set.
magnitude
phase

13. Active Low-pass Filter: Example
Problem: Design an active low-pass filter
Given Data: Av= 40 dB, Rin= 5 kW, fH = 2 kHz
Assumptions: Ideal op amp, specified gain represents the desired low-frequency gain.
Analysis:
Input resistance is controlled by R1 and voltage gain is set by R2 / R1.
The cutoff frequency is then set by C.
The closest standard capacitor value of 160 pF lowers cutoff frequency to 1.99 kHz.
and

14. Design Tools There are a number of design tools available online
Some, like Analog Devices and Texas Instruments are web-based
Microchip has a free downloadable tool
Many others pop up in Google

15. Microchip FilterLab www.microchip.com/filterlab
PC only – up to 8th order (and some other limitations)
Shows circuit, Transfer/phase, SPICE netlist
Allows limited capacitor selection

17. Parameter Selection

18. Type Selection

19. Summary

20. Magnitude and Phase

21. Circuit

22. SPICE Netlist

23. Analog Filter Wizard

24. TI Webench

25. Where To Find Them www.analog.com/designtools/en/filterwizard/

26. Variable Filtering?
Along with adding variable passive components, we can also design a variable filter such as a VCF, or voltage-controlled filter
One component of analog music synthesis (along with the VCO and others)

27. Voltage Controlled Filter

29. What About Design Changes, Etc?
What if there was a filter that you could change completely – from LP to BP, Butterworth to Chebychev, etc?
Of course there is – we have that power in digital filters, as well as many advantages as well as disadvantages. We will look at these for the next three days

30. 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

31. 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)