Passive RL Filter

Introduction: In this lab, we built a frequency filter using RL series circuit. We did not know what kind of filter this is at the start, but we were to find it out later using calculation and measurement.

Voltage of Resistor at 15915 Hz

Voltage of Resistor at 159150 Hz

Voltage across Inductor at 1591 Hz

Voltage across inductor at 15915 Hz

Voltage across Inductor at 31830 Hz

Voltage across Inductor at 159150 Hz

We measured voltage across resistor and inductor at tenth, eighth, fourth, second, itself, twice, four times, eight times, and ten times of corner frequency, that is 1591, 1989, 3978, 7957, 15915, 31830, 63660, 127320, 159150 Hz. The result is as below,

Voltage transform value means voltage gain.

We did not measure value for 31830 Hz.

We plotted Voltage gain vs. Frequency.

Conclusion:  Clearly Gain of resistor can be used as low-frequency filter and gain of inductor can be used as high-frequency filter. the gain of resistor and inductor have summing relationship. their gain together is 1. It is because the voltage across inductor and resistor together is input voltage. If gain of Resistor is 0.7, then gain of the inductor is 0.3.

Apparent Power and Power Factor

Introduction: In this lab, we set up the circuit it is given to us and make a minor change of different load resistor and measure its V and I rms.

At first, we calculated various data that was required

The setup.

With 10-ohm resistor, 

With 47-ohm resistor.

With 100-ohm resistor,

Summary: Our calculation was totally off the chart. It is said in the menu that we should use channel 1 to measure the input voltage but we measured voltage across 10-ohm resistor for R_t and used it to measure current and put input in Math channel 1, so we do not think this make much difference. When we were using 10-ohm and 47-ohm resistor in Load impedance, RMS of Voltage and Current did not change much, but when we used 100-ohm resistor, RMS voltage almost halved and current did not change much.

Impedance

Introduction: In this lab, we are going to apply voltage with different frequency to RR, RL, and RC circuit to measure current through each circuit.

                 First we calculated expected current in each circuit when amplitude of 2V and 5k frequency for supply voltage.

Expected current in each circuit.

In the following graphs, channel 1 (yellow curve) is voltage across 47-ohm resistor, channel 2(Cyan curve) is either 100-ohm resistor, capacitor, or inductor depends on which circuit, and Channel 3(Orange curve) is current through circuit.

1k frequency, 100-ohm Resistor

5k frequency, 100-ohm Resistor

10k frequency, 100-ohm resistor

With resistor component, voltages and currents are in phase and magnitudes did not change, but periods changed in different frequencies.

1k, Inductor Gain=0.1305, Phase= 278.1°

5k, Inductor, Gain=0.5381, Phase=27.365°

10k, Inductor, Gain= 0.7938, Phase=272.34

1k, Capacitor, Gain=1 Phase=89.424°

5k, Capacitor, Gain=1,Phase= 90.77°

10k, Capacitor, Gain=1, Phase= 86.76°

Summary: In all experiments, current is always in phase with voltage across 47-ohm resistor.
When we connected a resistor in series with circuit, the gain, amplitude did not change and 3 curves were all in phase. When circuit connected with an inductor, the gain increased with frequency and have certain phases. When circuit is connected with a capacitor, the gain was always one and also current increased as frequency increased.

RLC Circuit Response

Calculation

Phasors: Passive RL Circuit Response

Introduction: In this lab, we calculated current for RL circuit ran with ac current with it's voltage source. After that, we divided function of current with voltage to get gain of the circuit in three different angular momentum. We built the circuit and compared with calculated values.

We calculated gain of circuit when ω is 47k rads per second is 0.015, when it's 4.7k rad/s(ω/10), it's 0.0212, and 0.00212 when its 470k rad/s(10ω).

Unfortunately, we did not take picture of built circuit.

4.7k rad/s, gain of 0.0212 (Brown line) (it's shown it's at 0.212 because we are showing 10 times of measured value using 0.02A/div (Voltages are at 0.202V/div))

47k rad/s, gain of 0.015

470k rad/s, gain of 0.00212

Summary:  This lab gave us our expected values. every gains matched our calculated values. Notable points in this lab were at 4.7k rad/s, V_in and current were inphase, at 47k rad/s, they were all off-phase, and when ω was at 470k rad/s, V_in and V_L were in-phase.

Inverting Differentiator

In this lab, we are going to make Inverting differentiator and input sin wave in input voltage. We are going to calculate the estimated output voltage and finally, we are going to measure the output voltage at different frequency sin waves(at same amplitude).

We first calculated output voltage as a function of input voltage and time.

We calculated at what frequency we have gain of 1(V_o=V_in). We found that happens when the frequency is 234 Hz.

Setup(1)

Setup(2)

Setup(3)

We measured actual Capacitance and Resistance, it is 0.945 μF and 668-ohm respectively.

We measured output voltage at 500Hz, 250Hz, and 100Hz.

100Hz 1V

250Hz 1V

500Hz 1v

At the end, we calculated theoretical V_out and compared with the measured value. It has very small percentage of difference.

Summary: This lab went great, we got our estimated value. we calculated the circuit will have gain of 1 at 234Hz and we got gain of 1.1 at 250 Hz, so we would get value very close to 1 when we input 234Hz sin wave. We have higher gain in higher frequency because when we differentiate input voltage the angular velocity-omega will go out and multiply with amplitude due to chain rule. Omega can be also expressed as 2fπ, f stands for frequency.

Passive RC Circuit Natural Response

This morning I went to wake up my dog.

Start of this class we did some problems related to RC and RL circuits...

Problem(1)

Problem(2)

Starting Lab...

We first calculated the voltage across capacitor when it is fully charged and the times it takes to discharge 99% of charge.(It happens when time elapsed 5 times of time constant(tau). It was 0.0756 second. The actual resistance for 1k-ohm was .95k-ohm and 2.2k-ohm was 2.13k-ohm

We used Triggering and Single Acquisition feature from Appendix.

Discharge time we have got from two data point was -22.17ms(initial) and 118.6ms(Final).

Charge time we got from two data point was -5.13ms(initial) and 105.1ms(final), and max voltage was 3.48V which is very close to what we expected.

Summary:we calculated it will take 0.0756 second to fully discharge the capacitor, however, experimental value says it will take 0.14 second to discharge, twice of what we calculated. So there is mistake in our calculation or lab procedure. For time for it to charge, it was 0.11 second, but we did not calculate the times for circuit to fully charge itself.(we forgot and we thought we don't need it). We got our maximum voltage for capacitor correct, which we calculated to be 3.43V and measured amplitude is 3.48V.

Inductor Voltage-current Relations

Starting lab...
                 This lab is almost same with previous lab "Capacitor Voltage-current Relations", but we change capacitor with inductor and measure same thing in 3 voltage sources.

1kHz, 2V Sinusoidal input Voltage

2kHz, 2V Sinusoidal input voltage

100Hz, 4V triangular input voltage

Summary: It makes sense that all of voltage across inductor is very low because inductors resist change in voltage. So Voltage across them are low compare to input voltage. This lab I think we also messed up the input equation of current, or it might be very low. As for voltage in triangle wave, I think because the amplitude of wave is high again, so inductor want to resist its high slope of change and thus have very low voltage across it.

Capacitor Voltage-current Relations

First, we did some problems

Starting lab...
                In this lab, we are going to connect a resistor(100-ohm) and capacitor in series with sinusoidal voltage sources and triangle source and we are going to measure voltages across resistor and capacitor.
(Notes: sinusoidal voltage source can go through capacitors)

Setup(1)

Setup(2)

Graph of sinusoidal wave with 1kHz and 2V amplitude

Graph of sinusoidal wave with 2kHz 2V amplitude

Graph of triangle wave with 100Hz and amplitude of 4V

 Summary: In this lab we used both sinusoidal and triangle wave through circuit with resistor and capacitor in series. With its frequency increased in second measurement it is appeared that voltage difference between resistor and capacitor is decreased. It could be case of with frequency changing so fast that capacitor does not have enough time to charge to higher voltage. As for triangle wave, we could see it stops charging at certain times; it is because the amplitude of triangle wave is twice of voltage as before so the capacitors charge to its charging capacity and thus stop charging. For the curve of current(orange line), I think you typed the equation wrong in waveform or it could be very small ,so we could not see it is actually changing.