May 28

Signals with Multiple Frequency Components

In this lab, we will calculate the magnitude response of an electrical circuit and use this information to infer the effect of the circuit on some relatively complex input signals.

 There is an 90 degree angle delay of the output signal.

As the frequency increases, the output power decreases. 

May 26

Apparent Power & Power Factor

In this lab, we learned the use of apparent power and power factor to quantify the AC power delivered to a load and the power dissipated by the process of transmitting this power.

for  three different cases:

1. When transmission line resistance is 10 Ω (actual = 10.3 Ω)
2. When transmission line resistance is 47 Ω (actual = 47.2 Ω)
3. When transmission line resistance is 100 Ω (actual = 98.6 Ω)

This is how the circuit was connected.

After all the calculations, these are how the power dissipated when R = 10 , 47, and 100 ohms.

 case 1 R = 10ohms

 Case 2 R = 47ohms

 Case 3 R = 100 ohms

 When resistance of the transmission line R_T = 47.2 Ω, with 1uF capacitor in parallel with 1mH inductor

When resistance of the transmission line R_T = 98.6 Ω, with 1uF capacitor in parallel with 1mH inductor

When R increases, Apparent Power decreases.

May 14

Inverting Voltage Amplifier

In today's lab, we will be concerned with the steady-state response of an inverting voltage amplifier to sinusoidal inputs.

 At f = 100, 1000, and 5000 we calculated the gains and angles for the output.

This is how the circuit is connected.

This is the input/output data at f = 100

The angle is 27.7 and the gain is 0.87

This is the input/output data at f = 1000

The angle is 79.2 and the gain is 0.191

This is the input/output data at f = 5000

The angle is 90 and the gain is 0.05

As the frequency increases, the angle increases, and the gain decreases. 

May 12

Phasors: Passive RL Circuit Response

In today's lab, we will be concerned with the steady-state response of electrical circuits to sinusoidal inputs. We will measure the gain and phase responses of a passive RL circuit and compare these measurements with the calculations. 

 For w = 4, we found Zr = 10, Z1H = 4j, Z0.5H = 2j, Z 0.1F = -2.5j
We found Ix = 7.5<108.43

The picture shows the calculation is correct, at this frequency.
w = wc.

May 7

Impedance

In today's lab, we measure impedances of resistors, capacitors, and inductors. The measured values will be compared with the expectations values.

Zc = 1/(jwc)

Zl = jwlL

Zr = R

Zseries = Z1 + Z2 + Z3 .....

Zparallel = 1/ ( 1/Z1 + 1/Z2  + 1/Z3 + .......)

We setup three circuits each with a 47 ohm resistor in series with a resistor, an inductor, or a capacitor.

 From left to right: RC, RL, RR circuit.

There is no phase shift for the RR circuit.

 For the inductor the current lead the input voltage by around 90 degree. The frequency have affect on the angle.

For the capacitor, the input voltage lead the voltage across the capacitor by around 90 degree. The frequency have affect on the angle.

April 30

RLC Circuit Response

This lab will emphasize modeling and testing of a second order circuit containing two resistors, a capacitor, and an inductor.

a = R/2L = 550000,  Wo = 1/sqrt(LC) = 316228.

Since a > Wo the circuit is over damped

 With a square wave input, the voltage across the resistor R2 shot over the input voltage. then drop back down. It matches the prediction of an over damped circuit.

The pictures show how the circuit is connected.

April 28

Series RLC Circuit Step Response

In this lab, we will build and test a RLC second order circuit in series.

 C = 460nF, L = 1uF, R = 1.3ohm.
a = R/2L = 5.5*10^-5 Wo = 1/sqrt(LC) = 1.459*10^-6. a > Wo.
The circuit is under damped.

To make a = Wo which is critically damped, we need to use a 3.3uF capacitor.

The three elements are connected in series in RLC order.

As expected, the voltage across the capacitor shot beyond the input voltage then oscillate down to meet the input voltage.