Experiment 14Series RC Circuit

Circuit to be constructed

Shunt resistor

It is good practice to short the unused pin on the

trimpot when using it as a variable resistor

Velleman function generator

Note; 0.1 mF = 100 nF

Oscilloscopes can measure voltage as a function of time, but not current.◦ To measure time-varying current, we include a small

resistor at the bottom of the branch in which the current measurement is desired.

The value of the resistor chosen should be at least a factor of 10 times smaller than the other resistors in the branch.

The voltage across the small resistor divided by its resistance yields the current through the branch.

Current Measurement:Shunt Resistor

Measurement point for

input voltage

Measurement point for voltage across capacitor

Measurement point for current through resistor

where V(t)/10W equals

the current.

10

100nF

Transient Response:Period of Input Voltage ≥ 5t

Steady state values for the capacitor’s voltage and current are assumed to be reached by the time t = 5t.

Transient Response:Period of Input Voltage < 5t

The capacitor never fully charges or discharges. The maximum and minimum capacitor voltage oscillates around ½ of the voltage source connected to the RC combination. The range of the capacitor voltage depends on how small the period is compared to 5 . t The smaller the period, the smaller the range.

• Plot a graph of vC(t) versus t when the frequency of the square wave using Equations (7) + (8) form the background section for Experiment 14 in the lab manual.

• Plot a graph of iC(t) versus t, which is found by multiplying the capacitance by the derivative of Equations (7) + (8) from the lab manual. • Equations 7 and 8 are the general equations for the voltage across the capacitor

as it charges and discharges, respectively. Equations (2) and (3) are only correct when t ≤ 1/10 f.• You will have to do a piecewise calculation (i.e., switch from equation (7) to equation

(8) for the second half of each period of the square wave when writing your MATLAB code. • Examples are given in the Resources/Technical Support MatLAB folder on the course

Scholar site.

• You will run the program for the two different time constants and include all of the plots mentioned in the lab manual in the lab reports.

MatLab ProgramNote: change from instructions in lab manual

• Plot of the voltage across the capacitor as a function time– Use either Vpulse or Digclock as the voltage source

• Instructions on setting up a transient simulation using these sources are posted under Resources/Technical Support: Circuit Simulation

• Include the input voltage in the plot and show three periods.• Plot of the current through the capacitor as a function time

– Plot of the voltage across the shunt resistor divided by its resistance as a function time• Instructions on how to perform calculations in the PSpice plotting

routine are posted under Resources/Technical Support: Circuit Simulation.

– Use a current marker instead of a voltage marker• Show three periods.

PSpice Simulations:Transient Analysis

• Calculated using multiple methods:– Analytically (Step 1)– Experimentally after measurements of R, C, and Rshunt

• Note that you have the ability to measure capacitance on your digital multimeter.

– From a curve fit of v(t) as the voltage across the capacitor decreases when the input voltage changes from +5V to ground.• This is done for each time constant.

Time Constant of RC Circuit

• Set the Velleman function generator such that Vin is a square wave that swings from 0V to +5V.

• Settings for the square wave are 5V amplitude with 2.5V offset.• The duty cycle is 50%.• Frequency should be set to 1 kHz.

– Use DC coupling on Channel 1 and Channel 2• Ignore the comments in the lab manual about AC coupling

unless you select AC Coupling when performing the measurements.

• Ignore all comments about a sound card or the Zeitnitz oscilloscope software program.

Voltage Measurements

No credit will be given for step 32 so you do not need to complete this step.

No Extra Credit