Experiment # 3 EE 312 Basic Electronic Instrument Laboratory September 13, 2000 See Lecture 5 Filters on 1999 EE 312/352 Website

Objectives: Design and assemble of Resistance- Capacitance (RC) and Resistance- Inductance (RL) filters. Measure the frequency response (magnitude & phase) of RC and RL filters. Examine the time-domain responses of these filters to a square-wave voltage.

Background: R Impedance

RR High-Pass RL Filter Low Pass RL Filter High-Pass RC Filter Low-Pass RC Filter High Low High

time 0 V out (t) R 0 V in (t) Example: Low-Pass RC Filter 0

? & Phase shift ? time 0 V out (t) R 0 V in (t) Low-Pass RC Filter

Calculation for a High Pass Filter (Steady State Response) R -jXc

but Define crossover frequency, f x, as Then so First, look at this factor f x, roughly speaking, is the frequency that separate the frequency range for which a filter passes signals from the range for which the filter attenuates signals

1 Phase shift

so: or Amplitude Phase

When f >> fx, Amplitude 1, 0 Thus, this is high pass When f << fx, Amplitude 0, 90 Low frequencies are blocked

Step Response High-Pass Low-Pass V in V out V in Voltage on capacitor cannot change instantaneously. So V out = Vin initially. Voltage on capacitor cannot change instantaneously. So V out = 0 initially. V in V out V in V out

Fall Time V out time % 90% 100% 1/e~37% Fall Time & Time Constant

Relationship Between Time Constant T & Rise-Time or Fall-Time T = RC or L/R Rise-Time (Fall-Time) = T X ln9 = 2.2T

Components: Resistor Substitution Box Capacitor Substitution Box 1 mH Inductor 100 Ohms Resistor

R Function Generator oscilloscope FilterScopeOscillator FG has 50 ohm internal resistance- keep R high enough so that crossover freq. has no more than a 10% dependence upon it. e. g. R > 500 ohm CRO has 1 M input impedance - keep R low enough so that crossover freq has no more than a 10% dependence upon it. R < 100k Choose C so that crossover frequency fx = 1/(2  RC) is well within FG frequency range. E.G. fx ~ 3 kHz. Comment:

Procedures: 1- Determine internal impedance of the function generator which is expected to be ~50 ohms 2- Measure low-pass RC filters characteristics 3- Measure low-pass RL filters characteristics 4- Simulate RC & RL low-pass filters (Bell 242) 5-Measure time constant and fall time in a high- pass RC filter using a square wave 6- Measure time constant and rise time in a low- pass RL filter using a square wave

1- Internal Impedance of Function Generator Filter impedance >> Generator impedance R load > 10 X R internal R internal R Load Function Generator

Step 2- Measure the decreased amplitude of the output signal and I x with 100 ohms resistor R internal Function Generator oscilloscope 1M Step 1- Set V p-p =10V Step 3- Determine R internal R internal 100 Function Generator oscilloscope IxIx

2- Low-Pass RC Filter ~ CRO CH2CRO CH1 Assemble a low-pass RC filter having a Crossover frequency of about 3 kHz R C

~ CRO CH2CRO CH1 V p-p =10V V out Frequency..fx....fx.. a) b) Use Digital CRO to readout directly phase difference between input and output

3- Low-Pass RL Filter ~ L=1 mH R V out V in Repeat the procedure in step 2 for an appropriate crossover frequency in the range 100 kHz to 150 kHz.

4- Simulation (PSpice) Simulate the RC and RL low-pass filters in parts 2 and 3. Do so in Bell 242. Perform an ac sweep between frequencies of 1Hz and 1 MHz (or from fx/100 to 100 fx) with 20 to 50 data points per decade. Display experimental and PSPICE values for the magnitude (dB) and phase of the output voltage on the same graph.

5 - Time Constant and Fall Time in a High-Pass RC Filter to oscilloscope V out V in R C Measure the time constant and fall time. Use Digital CRO to readout directly fall time. Use Digital CRO Cursors to determine T = RC

6- Time Constant & Rise Time in a Low-Pass RL Filter L=1 mH R V out V in Measure the time constant and fall time. Use Digital CRO to readout directly fall time. Use Digital CRO Cursors to determine T = L/R