PHYS245 Lab: RC circuits

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1 PHYS245 Lab: C circuis Purpose: Undersand he charging and discharging ransien processes of a capacior Display he charging and discharging process using an oscilloscope Undersand he physical meaning of he C consan Measure he C consan using he oscilloscope Use he C circui as a low-pass filer and measure he ransfer funcion Equipmen lis: ELVIS ΙΙ, 5.0 k resisors, and 4.7 nf capacior, jump wires, banana-o-minigrabber cable, coaxial cables esisor-capacior circui (C circui) is widely used in elecronics as a filer circui. I is essenial o undersand how a C circui funcions. In his Lab, you will have a chance o periodically charge and discharge a capacior using a square wave and visualize he charging and discharging process on he Scope. The C circui can be used as a low pass filer. You will measure he ampliude of he oupu signal as a funcion of he frequency and plo he graph in Origin. 1

2 Pre-Lab Exercises Thoroughly read hrough his manual and pracice circui consrucion on he prooyping board picure on nex page. For a 4.7 nf capacior and a 5.0 kω resisor, calculae he C ime consan. Answer he following quesions: The longer he C ime consan, he longer i akes o charge or discharge he capacior, rue or false? The square wave in experimen Ι is used o charge and discharge he capacior periodically, rue or false? For a capacior and a resisor in series, mos of he a.c. volage drops on he capacior a very high frequency, rue or false? 2

3 3

4 Experimen Ι: Charging and discharging a capacior and C consan The following figures are quick summary of wha you have learned in he lecure in regard o charging and discharging a resisor V 0 C V 0 2 C v() v 1 ( ) ε e = C Charging discharging v = εe v C () ( ) C ε 0.63ε =C=τ 4

5 However, i is difficul o conduc an experimen based on he circuis in he previous page. Because he charging or discharging process happens during very shor ime scale (< millisecond). If you wan o display he capacior volage as a funcion of ime on he Scope, you have o choose fas scan speed (a shor imebase) o resolve he change of volage on he shor ime scale. Bu even if you do choose a shor imebase, he image will disappear from he Scope before you can see ake a look, since he Scope scans fas. So one possibiliy is o charge and discharge he capacior periodically a very fas pace. Imagine you oggle he swich back and forh rapidly. Wih repeaed occurrences of charging and discharging, i is possible o have a sable image on he Scope (like a waveform) by using Edge rigger on he Scope. Bu i is impossible for you o oggle he swich back and forh in less han a millisecond. Now a beer way o do his experimen is shown in he figure below. inpu oupu To FGEN C To Scope A square wave is delivered by FGEN. The volage swiches beween V o and 0 periodically. This is equivalen o oggling he swich beween 1 and 2 in he figure on previous page. Capacior volage as a funcion of ime can be displayed on he Scope 5

6 To Scope Ch0 inpu To FGEN oupu To Scope Ch1 C By using a common ground, he acual circui on he board can be furher simplified, as shown on he lef. You are given a 5.6 kω resisor and a 4.7 nf capacior. Build a C circui according o he above diagram. Deliver a 3 khz square wave signal wih 2 V peak-o-peak volage from he FGEN clip on he disribuion sripe o he inpu of he C circui. oue he oupu signal from he capacior o BNC #2, and hen o Scope Ch1 by a coaxial cable. Display he waveform on he Scope. As a comparison, you wan o see original inpu square wave. You can roue he inpu signal from FGEN clip o he BNC #1 clip by jump wire, and hen o Scope Ch0 hrough coaxial cable. Display boh Ch0 and Ch1 on he Scope. Adjus Verical Posiion for Ch0 o offse he square wave verically. This way, he inpu and oupu waveform are shifed verically, and allows for a beer comparison. emember o adjus imebase and sensiiviy scale o have proper viewing of he signals. Sar wih Immediae Triggering mode, which means no paricular riggering. Once you ge clear waveform (which is moving on he screen, swich o Edge rigger mode. A sable image can be obained. 6

7 The screen sho on he righ shows he inpu square wave signal and he oupu on he capacior. 7

8 Now disable Ch0 by unchecking Enable of Ch0. Adjus he Vol/Div value, so ha he waveform in Ch1 occupy mos of verical scale, bu does no go beyond he limi. This is o maximize he accuracy of he following measuremens. From he Ch1 oupu waveform, ry your bes o esimae he ime consan of his C circui. efer o he following picures for reference. v() ε v C () ε 0.63ε 0.37 ε =C=τ τ In he charging curve, The ime i akes o charge o he 63% of he full volage equals o he C consan τ. In he discharging curve, he ime i akes o discharge o 37% of he full volage (losing 63%) equals o he C consan τ Compare he measuremens wih he calculaed C consans. Change he frequency of he inpu square wave, and pay aenion o he change of he oupu signal. 8

9 Experimen ΙΙ: Use C circui as a low pass filer To Scope Ch0 inpu Oupu o Scope Ch1 To FGEN C The C circui can be used as a filer. The above circui, which you have used, can ac as a low pass filer. The circui is he same as he one you have used in par 1. Bu in his experimen, send in a sine wave as inpu. The oupu is also a sine wave. Bu he magniude and phase is differen from he inpu sine wave. Measure he ampliude as a funcion of he frequency. Plo he resuls in Origin. 9

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