series rc circuit. shunt resistor it is good practice to short the unused pin on the trimpot when...

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