1. Active Filters

2. This is not in the lab manual While the circuit that will be used is very similar to the one described in the lab manual, the steps in the lab procedure are significantly different. – Please follow the laboratory procedure posted in the Week 9 module.

3. Passive Bandpass Filter Cascading a RC (or RL) low pass filter with a RC (or RL) high pass filter LC filter

4. Active Bandpass Filter While an active bandpass filter can be constructed by cascading an active low pass filter with an active high pass filter, there are designs that use only one op amp.

5. Active vs. Passive Filters The maximum magnitude of the voltage transfer function of a passive filter is at best equal to 1. – Parasitic resistances and capacitances in RL can make this value considerably lower. Active filters incorporate amplifiers with the filter elements so that the filter has gain. – Maximum of the voltage transfer function can be greater than 1. – f o limited by frequency of the operational amplifier

6. The transfer function for the active bandpass filter is where

7. Goal of Experiment Use active filter to remove specified Fourier components from a square wave voltage source. T is the period of the square wave

8. Summation of Fourier Components

9. Bandwidth The difference between the frequencies (in Hz) where the power is ½ of the maximum output power – Maximum power to output occurs at f o

10. Order of the Filter The magnitude of a voltage transfer function of filter will decreases at a rate of -20dB per decade times n, where n is the order of the filter.

11. PSpice There is a DB macro or you can put in an equation into the Trace Expression to calculate -20 log (V o /V in )

12. MATLAB Note that you need to specify the frequency range for the bode plot. – The default is radians/s for the bode plot – Help on bode plots explains how to define the frequency range over which the plot is performed.

13. Velleman Spectrum Analyzer

14. Voltage/Frequency Measurement