# Active Filters

The lab is getting  messy.  Make sure you read the lab rules about keeping the lab clean.  In particular, put away all components, wires and connectors when you are done.

You need to start thinking about your final projects!

This week you will explore the world of active filters.  You should read the Introduction to Frequency Response and Active Filters, and the Introduction to Switched Capacitor Filters before coming to lab.

## To Do:

### 1) Op Amp Filters  • Hook up the circuit with R1=1 MΩ, R2=100 kΩ, C=0.01μF. Use supply voltages from ±12 to ±15V.  Measure Vo/Vi (magnitude as well as phase) for at least ten frequencies between about 10/R1C and 0.1/R1C. Compare these results with what you expected. Don’t forget to convert from radian frequency to Hertz (ω=2πf).  You need not include any oscilloscope printouts for this part (input and output should both be sinusoids).  You can use the oscilloscope to make many of the measurements (frequency, magnitude...) of the input and output voltages.

## 2) Switched Capacitor Filters

a) In this lab we will finish populating your circuit board.  You may want to refer to page 3 of the schematic and the layout. On your printed circuit board add (* indicates that polarity is important)

• 14 pin IC socket (U10)*
• 2 pin header (J7, JA5)
• signal diode (e.g, 1N914) (D3)*  - not a power diode.
• 1MΩ resistors (R9)
• 100kΩ resistors (R7, R8, R10)
• 10kΩ resistors (R11)
• 47kΩ resistors (R12)
• 2425/2426 rail splitter (U7)*  -  this is on page 1 of the schematic
• 0.001μF (C12)
• 1μF (C13) * (this may or may not be polarized)
• Add test points as necessary.

b) At this point, apply power to the board. You'll need to use external power to get the 5V needed to supply the analog circuitry. Measure the voltage at J2.5; it should measure 2.5 volts.

c) Now add the LTC1059  IC.

The 2nd order switched capacitor filter in the LTC1059 is equivalent to those on the LTC1060 (but the LTC1059 only has one second order filter instead of two, and the LTC1059 has an extra op-amp).  The filter is configured in mode 1 (page 11 of data sheet - you may also want to refer to equations for specific transfer functions on page 9 and page 10))  Note that the diagram for the LTC1059 in the data sheet is wrong.  The correct diagram is shown below:

 Incorrect Correct  d) Place your daughterboard on the MSP430 LaunchPad board and use code to set pin P1.4 (SMCLK) to oscillate at 500 kHz (in a previous lab you set this to 250 kHz).

e) Measure the frequency of the signal at pin P1.4  It should be 500 kHz.

f) Set up a signal generator to give about 2 volt peak to peak 10 kHz sine wave centered around ground (no DC offset) and attach it to the testpoint labeled JSig1 through a 100μF capacitor as shown (don't forget a common ground): The voltage at JSig1 should look like the function generator output but centered about 2.5V instead of ground.

g) Verify that the output labeled JBP is a bandpass output and take enough data to estimate HOBP, ωo and Q.  Take at least 10 measurements spanning at least a decade above and below ωo.  Use gain only (measured by peak to peak voltages), no phase data is necessary.  Take more data when the gain is changing rapidly with frequency so you can show details of the response.You will need this data for the writeup.

h) Get at least one screen shot that shows the discrete nature of the output voltage.  You will need to expand the time base for this.

i) Determine what C13, R12 and D3 do.  Examine JDet as the frequency is swept across ωo or as the amplitude of the input is changed.

j) Change the input to a 100Hz square wave and plot the step response of the circuit at JBP

k) Keep the input to a 100Hz square wave and plot the step response at JLP.

l) Change the code to get a 250 kHz signal at pin P1.4.  Repeat part k.  Note any differences.

## To Turn in:

### 1) Op Amp Filters

1. Your derivations of the transfer function for the low pass filter circuit.
2. Include data that verifies that the circuits work as expected.  Compare measured to expected values of magnitude and phase as a function of frequency (i.e., put your data on a Bode plot that shows the expected filter response (magnitude and phase) - use MATLAB's "bode" function).  Both your data and the expected results should be on the same graph - if you have trouble doing this, please let me know.

### 2) Switched Capacitor Filters

1. Derive the transfer function of the switched capacitor filter and verify the equations for HOBP, ωo and Q from the data sheet.
2. Include your data from the band-pass output (part g) that you used to determine HOBP, ωo and Q, along with the expected output of the filter with those parameters derived from circuit components and the data sheet ("bode").  Both your data and the expected results should be on the same graph - if you have trouble doing this, please let me know.
3. Show the discrete nature of the output voltage.  Verify the clock frequency of the switched capacitor filter from your screen shot.
4. What do C13, R12 and D3 do?  What is the RC time constant for C13 and R12?  What would happen if the RC time constant was much larger or much shorter?
5. Show the step response at JBP.  Compare it to the expected step response ("step").
6. Show the step response at JLP.  Compare it to the expected
7. Your data from the step response (part l - the 250 kHz clock) along with an expected result (MATLAB).