ECE 240 - Experiment 9-First Order Circuits PDF

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ECE 240 - Experiment 9-First Order Circuits
build first order circuits that contain a resistor with a capacitor or a resistor with an inductor. We see how voltages of a capacitor or an inductor changes over time by using a function generator as a source of a circuit. Also, in this experiment, ...

Description

Spring 2017

California State University, Northridge Department of Electrical & Computer Engineering

Experiment 9 First Order Circuits

April. 18, 2017

ECE 240L

1. Introduction: In this experiment, we will build first order circuits that contain a resistor with a capacitor or a resistor with an inductor. We see how voltages of a capacitor or an inductor changes over time by using a function generator as a source of a circuit. Also, in this experiment, we will compare a time constants that we got with time constants that we calculated. After that, we compare values that we calculated with values from a measurement.

2. Equipment Used: Type

Model

DC Power Supply

E 3630A

Digital-Multi-Meter (DMM)

CDM250

Serial No.

Calibration Date

Oscilloscope Function Generator Proto-Board 3. Parts Used: QTY

Component

Value

Type

1

Resistor

470Ω

Carbon, +/-5%

1

Resistor

680Ω

Carbon, +/-5%

1

Resistor

6.8KΩ

Carbon, +/-5%

1

Capacitor

0.1μF

Tantalum, +15V

4. Software Used: Pspice Released Version: 16.0.0.s001 MS Office 2010

5. Theory: When we mention first order circuits, we have to know that these circuits contain a capacitor with a resistor or an inductor with a resistor only.

● Voltage-Current for a Capacitor in First-Order Circuit

These formulas above are used to calculate voltage and current passing through a capacitor. C is a capacitance of a capacitor. For a formula 9.1, VC(-∞)=0, so that we can ignore this value so that we can have a formula without Vc(-∞) (9.3).

(9.3) For a DC circuit, a current passing through a capacitor is 0 (short circuit) because dv/dt=0. Because of this condition, a capacitor can be replaced by an open circuit. ● Voltage-Current for an Inductor in First-Order Circuit

(9.4)

(9.5) These formula aboves (9.4) and (9.5) are for an inductor and a resistor in a first-order circuit. For 9.4, voltage is equal L(inductance of a inductor) multiplies by di-L/dt. We assume that Io=0 at the beginning so that we can have another formula for iL (9.6).

(9.6) Under a DC condition, we have a current crossing an inductor is constant so that a voltage passing through an inductor is zero. It is a reason why we can replace an inductor by shorting a circuit under a steady state condition of a circuit. ● Simple RC and RL Circuits ❖ For a RC circuit and RL circuit, we have to consider a value time constants of a capacitor and an inductor. ❖ For a RC circuit, a time constant is て=RC (Unit: second (s)). ❖ For a RL circuit, a time constant is て=L/R (Unit: second(s)). ❖ In DC circuit, it takes 5て (5RC or 5L/R) to fully charge for a capacitor or energize an inductor. 6. Procedure and Results: Circuit 1 ➢ Build the circuit below to find out the internal resistance of the function generator (Rint) ➢ Set the frequency to 2kHz and measure the open circuit voltage. ➢ Then add a 100Ω resistor and measure the voltage.

Results and calculations Voc  = 5.12 V

VR = 3.44 V

RL = 100Ω

Rint = RL (Voc - VR) /VR  = 100(5.12 - 3.44) / 3.44 = 48.44Ω Rdc=(R/(1-VL))*VL=(100/(1-0.43))*(0.43)=75.44 Ω Circuit 2 Part A ➢ Build the following circuit using R= 470Ω resistor and a capacitor of 0.1μF. ➢ The frequency should be 2kHz square wave of 1Vpp ➢ Record VC(t) using oscilloscope and calculate the time constant.

Results R = 470Ω

With Rint, 5てt =  252μs (Measured) てcalculated= (Rint+R)*C=(48.84Ω+470Ω)*(0.1*10^-6)=5.1884*10^-5 (s) 5てcalculated=259 μs

PSpice data

Part B ➢ Replace the resistor on the previous circuit to a 6.8KΩ and a capacitor of 0.1μF. ➢ Adjust the function generator to an adequate frequency ➢ Record Vc(t) and calculate the time constant. Results R = 6.8kΩ f=800Hz 5てmeasurd=680 µs てcalculated=5てcalculated=(Rint+R)*C=(48.84Ω+6.8*10^3)*(0.1*10^-6)=6.85 µs

PSpice data

Circuit 3 ➢ Build the circuit below with a 680Ω resistor and an 68 mH inductor. Set the wave to 1 Vpp square wave. ➢ Adjust the frequency of the function generator for an adequate value. ➢ Record the voltage and calculate the time constant and compare it with the values from the pre lab.

Results Rdc = {R/(1-VL) }VL = {100/ (1-0.43)} 0.43 Rdc = 75.44Ω てmeasured=600 µs てcalcualted=L/(R+Rint+Rdc)=(680*10^-3)/(680Ω+48.84Ω+75.44Ω)=8.455*10^-5 (s) 5てcalcualted=423 µs

PSpice data

Ak

7. Conclusion: In this experiment we learned to build first order circuits with inductors and capacitors. From these circuits, we know how a capacitor charges and how an inductor energize. Also, we can compare a time constant that we got from a calculation with the one we measured. We believe that we can apply this knowledge to next experiments....