Day Twenty-Five and Day Twenty-Six - Passive RL Filter

On day twenty-five, we talked about transfer function and how they are used in for frequency response. Also, we talked about series and parallel resonance.

Given a transfer function above, we are able to approximate the curve of the H vs frequency and angle vs frequency.

That is how the curves look like.
Graphing Technique: We first draw the curve of each part, then we add up each part at one point to represent the final value of that point.

Resonance is a condition in an RLC circuit in which the capacitive and inductive reactances are equal in magnitude, which implies a purely resistive impedance.


On Day Twenty-Six, we talked about filters, YOHO.!!!
Filters is a very important component in electronic because it enables us to perform many things such as discriminating signal. There are four basic types of filters - high pass filter, low pass filter, band pass filter, and band stop filter.
The designated function of these filters is to pass a particular range of frequency signal and attenuate other frequency.
Low pass filter will pass low frequency(C in RC Series or R in RL Series), high pass filter (R in RC series)will pass high frequency, band pass filter (R in RLC Series)will pass middle frequency, and band stop filter (LC in RLC Series)will pass frequency other than the middle frequency.

Pre-Lab:

From the given circuit above, we calculated the cutoff angular frequency of the schematic will be at 1*10^5 radi/s = 15915Hz.

Result:
Before cutoff frequency (Resistor Voltage)

As we can observe from above graphs, the frequency before the cutoff frequency will have approximately the gain of one and a bit of phase shift.

At the cutoff frequency and after:

After cutoff frequency, we can observe that the gain start decreasing and there are phase shifts. This results from the imaginary part of the equation (the omega is not zero anymore).

Before the cutoff voltage (inductor voltage)

We can observe that before the cutoff voltage, there are phase shifts, and the gain is less than one.

In and after the cutoff frequency:

We can observe that as the frequency approaches infinity, the gain of the voltage approaches close to one.

Data:

Here is the data we measured and calculated.

Comparison:

Above are the graphs for phase vs frequency and transfer function vs frequency of the voltage output of the resistor.

Above are the graphs for phase vs frequency and transfer function vs frequency of the voltage output of the inductor.

Summary:

From the data graph above, we can conclude that the resistor voltage acts like a low-pass filter while the inductor voltage acts like a high-pass filter. However, from our data graph, we can see that the experimental gain of the voltage has a big difference with our theoretical gain, but the trend of the gain is almost the same; therefore. we can still conclude that in passive RL circuit, R acts like low-pass filter while L acts like high-pass filter.

Day Twenty-Four - Signals with Multiple Frequency Components

Hello guys, today we talked about transfer function.
The transfer function is simply the ratio of some output to some input in a given frequency.
From the transfer function, we can know more about the ratio of something over something with different frequency.

Since the range of frequency is wide, a Bode plot is used instead to simplify the range of the frequency.
One important point to note is that 10log is used for power while 20log is used for current and voltage.

Here is an example of how we calculate the transfer function of the circuit above.

Pre-Lab:
The response of the circuit with 2 680 ohms resistors and 0.1microFarat capacitor has the following result:

From the data above, we can conclude that as the frequency increases, the voltage gain decreases.

Result:
The voltage output and input have the following signals.

The yellow indicates the output voltage across the resistor, and the blue indicates the input voltage of the circuit.
As we can observe, the waveform has a shape of multiple waveforms into one waveform, and the voltage input and output have the similar pattern. We can also observe that low frequency signal has a bigger magnitude of gain while a high frequency signal has a smaller magnitude of gain.

Using the sweep function of the waveform, we get:

 This graph shows the gain of different frequencies signal, from 100Hz to 10kHz.
We can also tell from the graph that when the frequency is low, the gain is relatively small, and when the frequency is high, the gain is relatively big.

Summary:
The transfer function can give us a very intuitive meaning of how the circuit will respond when the frequency increases or decreases. Another important point to note is that in Part a, the three waveforms are combined together to generate one waveform, and the shape of the three waveforms are still observable. For the circuit we used in our lab, we can conclude that the circuit is a low pass filter because it has a high gain in low frequency but low gain in high frequency.

Day Twenty-Three - Apparent Power and Power Factor

Hey guys, today we continue to talk about power, especially on complex power and power factor.

The purpose of this lab is to see the complex power on the circuit.

Pre-Lab:

Above is our calculated values of the circuits with R(load) = 10, 47, 100 ohms.

Lab Result:
Our resistors have the values of 9.8, 47.1, and 99.3 ohms.

With the ten ohms resistor,

Our rms values of load voltage is 627mV, and the load current is 18.7mA with the phase difference 64.44 degree.

With the 47 ohms resistor,

Our rms values of load voltage is 625mV, and the load current is 10.68mA with the phase difference 36.828 degree.

With the 100ohms resistor

Our rms values of load voltage is 660mV, and the load current is 6.22mA with the phase difference 12.6 degree.

Comparing the values:

Summary:
From the graph above, we can conclude that our experimental value and theoretical value falls into similar values, so we successfully verify the apparent power equation Irms*Vrms = Power, and the power factor is cos(V-I). We can even conclude that even with the same amount of reactive element, changing the resistance value will change the phase because the real part is changed.

Day Twenty-One - No Lab, Day Twenty-Two - OP AMP relaxation oscillator

On day twenty one, we talked about how to analyse the circuit with AC signal using the old tricks we learnt in DC signal, all technique still apply to AC.

Hello guys, we talked about power today, WOOWWWOW.
Complex power sounds interesting, and the power factor is also interesting.
The power can be calculated by using the equations:

Also, today we talked about relaxation oscillator. Oscillator is a device which transform DC signal to AC signal. Without the existence of oscillator, AC signal will not exist.
A very simple design of oscillator is using op amp (comparator) and capacitor.
When the capacitor is charging toward the Vcc, the op amp switches, and output voltage saturates at
-Vcc. When the capacitor is charging toward the -Vcc, the op amp switches, and output voltage saturates at +Vcc, and this process will continue.

Pre-Lab:

We are planning to create a signal with the frequency 254 Hz; therefore we designed the belta value is 1/2, and we calculated the required resistor should approximately have 18k ohms.

EveryCircuit Model:

By implementing the circuit in everycircuit, we have successfully proven that the circuit will provide an oscillating signal.

Our measured value of frequency in our oscillator is 1/0.003740 = 267.3Hz.

Comparing to the theoretical and measured value, I think we have a good result with a small percentage error,  5.23%.

Summary:
One important point to note is that the average power absorbed by L and C are zero. Power in AC circuit involves both real and complex part, and the real part of the power has the actual meaning of power (Watt) while the complex power is just the "power" for the reactive elements.
Our lab, oscillator is a useful tool to create an AC signal, and the concept behind this device build up on our understanding from op amp and capacitor.

Day Twenty - Impedance 5/16/17

Hello guys, today we talked about impedance, which is the resistance in AC circuit.
The one special thing about impedance is the ability of making a phase shift.
For resistor, there will be no phase shift, but for capacitor and inductor, there will be phase shift due to its imaginary part impedance.


Here is an example of how we calculate the impedance of the capacitor and the alternating current going through it.

Pre-Lab:

For the circuit in the pre-lab for 5k Hz waveform, the calculated voltage and current for 47ohms plus 100ohms resistors is listed in one. The calculated voltage and current for 47ohms resistor and 0.001H inductor is listed in two. The calculated voltage and current for 47ohms resistor and 0.1microFarat capacitor is listed in three.

Lab:
For 5k Hz:

Our measured current is 13.27mA for 100ohms resistor and measure voltage is 1.367V.
There is no phase shift.

Our measured current is 34mA for the inductor and voltage is 1.06V.
There is a phase shift of 32.5 degree.

Our measured current is 6.2mA for the capacitor and voltage is 2.05V.
There is a phase shift of 82.8 degree.

Comparing the current and voltage:

Summary:
From our lab, we can conclude that there are phase shifts in circuits consisting of capacitor and inductor. Using the phasor analysis, we can precisely calculate the max current and max voltage in the given circuit element. It is important to note that the phase shift is also calculated, and it can be represented as the phase between voltage and current.

Day Nineteen - Phasors: Passive RL Circuit Response 5/11/17

Hello guys, today we talked about Phasor. wow.
Phasor is usually used in AC analysis.
Phasor is usually represented by complex number (rectangular), polar form R(angle), and exponential form.

In our calculation, the phasors are always calculated through the rectangular and polar form.

Note that, when we are adding the phasors together, phasor with different frequency(or omega) can not add up together.

This cheatsheet is very important.

Lab:

Pre-Lab

The cutoff frequency for 1mH and 470Ohm resistor is 47000/2Pi = 7480Hz
The frequency with one tenth of cutoff frequency is 748Hz
The frequency with ten times of cutoff frequency is 74800Hz

With ten times the cutoff frequency, the phase difference is (3.102)/(13.5)*360 = -82.72degree,
and the gain is 2.155(mA)/223.2(mV) = 0.009655

With the cutoff frequency, the phase difference is (16.87)/(135)*360 = -44.9degree,
and the gain is 13.28/668.3 = 0.01987

With one tenth of cutoff frequency, the phase difference is (0.03)/1.45 = -7.448degree,
and the gain is 0.001675/1.013 = 0.0016535

Comparing our calculated values with measured values:

From the data, I can conclude that we successfully finished the lab, especially on the phase difference, we have an excellent data. However, things can improve, especially on the small angle. For the small angle, a more precise data can be achieved for analysis for less error.

Summary:
Today, we talked about phasor for AC circuit analysis, and we finished the lab which describe the nature of phasor. The phase difference occurs depend on the element in the circuit. and with different frequency, we may have different phase difference and gain.