5-19: Maximum Power

Today prof Mason  showd us how to determine the power that delivered by AC source.

For this picture,  Professor Mason used  the same voltage for AC power and DC power. The bulb powered by AC source is dimmer than the bulb powered by DC source. 

When professor Mason turns the voltage for AC to about 1.4 times of the DC power, they seems the same bright. The Peak voltage of AC source is about 1.4 which is roughly square root of 2 times the voltage of DC source,

5-28:Signal with Multiple Frequency Component

Today we thought about what happens to circuit elements as the frequency increases.

The graphs show what happens to the impedance of those circuit elements as the frequency is increased.

 The goal of the experiment was to calculate the gain, so the voltage across the resistor was divided by the input signal, and we were left with our formula for our voltage divider. This formula came to be realized as shown below. 

This picture show that the  the gain in the output signal decreases as the frequency increases

The input voltage is a sinusoidal sweep from 100Hz to 10 Khz in 20 msec:

For this lab, we learn about the frequency response of a circuit is determined by the variation in its behavior with change in signal frequency.

5-26: Apparent Power and Power factor

This lab is about power and power factor to quantity the AC power delivered to a load and power dissipated by the process of transmitting this power

This the formula for the power factor. The apparent power is denoted S and it is the product of V rms and I rms. We can also describe the average power as the product of the power factor and the apparent power.

Pre-lab, we used the R2 at different value to get the theoretical values.

Follow the handout, the circuit we build for this lab

The oscilloscope screen with 10 ohm resistor

The oscilloscope screen with 47 ohm resistor.

The oscilloscope screen with 100 ohm resistor

the oscilloscope screen with 10 ohm resistor with a capacitor

the oscilloscope screen with 47 ohm resistor with a capacitor

the oscilloscope screen with 100 ohm resistor with a capacitor

when we add a capacitor in series with resistor. 

For this lab, we learned about apparent power and power factor. and we can  add a capacitor to reduce the phase shift  it could increase the apparent power. 

5-14: Inverting Voltage Amplifier

Inverting Voltage Amplifier Lab

In this lab, we measured the gain and phase responses of an inverting voltage amplifier circuit, and see the amplitude gain and phase difference between the output and input signals of a inverting voltage amplifier circuit. Then compared the measurements with expected values.

Here we are given the circuit diagram, and used the node to get the relationship between  the Vin and Vout.

We are calculating what the gain and phase angle will be at different frequencies.

        

When  frequencies is 100Hz, the waveform for Vin(red), and Vout(blue).

When  frequencies is 1000Hz, the waveform for Vin(red), and Vout(blue).

When  frequencies is 5000Hz, the waveform for Vin(red), and Vout(blue).

The built circuit consists of 2 Resistors (10kOhm), 1 Capacitor (1 microF), 1 Op Amp (OP 27), and a Analog Discovery device to provide input and measure output:

Here we see a direct comparison between our theoretical and experimental gain and phase shift angles. We can see that the percent error is small and acceptable for the most part. As a relatively quick experiment, we are pleased with our results.

Op Amp Relaxation Oscillator 

The purpose of this lab is to construct a relaxation oscillator, which is a type of device that will act as a switch when a certain voltage is applied to one of its terminals. This voltage is usually the voltage across a capacitor that is being charged or discharged. we use the last 3 digit for student Id is: 155, and get the R values.

For the first time, We got the Graphics is not very ideal which is not a perfect square waveform. 

After we reconnect the wires, we get what we want the perfect square waveform. 

Summary:

Today we went over how OP Amps work in AC circuit, and did  a new way to see how oscillators within circuits worked.

4-9 : Temperature Measurement System Design

Temperature Measurement System Design

We did following problem of cascaded op amp. A cascade connection is a head to tail arrangement of two or more op amp circuits such that the output of one is the input of the next.

Lab: After doing a bunch of math, we found out Vab = -(Vs/4R)*delta(R) .

         We measured the resistance of thermistor at room temperature (20 degree ) = 11.8k ohm, and we set that for Rnom.  And now we set the potentialmeter to 11.8k ohm and the rest of resistor to 11.8 K ohm as well.

 we set the potentialmeter to 11.8k ohm, and get the out range 0.00v~ 0.276V. 

Construction of the Wheatstone bridge 

Summary: This lab illustrates that Wheatstone bridges can be used to effectively relay minor changes in resistance, and then difference amplifiers can greatly magnify that difference. The lab was a success.

4-14 : Capacitor Voltage-Current Relations

Capacitor Voltage-Current Relations

 We sketched capacior voltage and capacitor current sinusoidal wave and triangular wave  using the capacitor voltage current relations. Because the current is equal to dv/dt, we anticipated the oscilloscope to detect Voltages and currents  as such:when current is positive , voltage is negative and vise versa. 

The dispay date for C1(top) A=1.032V the signal for the input voltage,  C2(under)  A= 1.626V the voltage across the capacitor,  M1(mid)  the current through the resistor,  when f=1kHz, A=2V, and Offset=0V

The dispay date for C1(top) A=1.452V the signal for the input voltage,  C2(under) A=1.178V the voltage across the capacitor,  M1(mid)  the current through the resistor,  when f=2kHz, A=2V, and Offset=0V

The dispay date for C1(top) the signal for the input voltage,  C2(under)  the voltage across the capacitor,  M1(mid)  the current through the resistor,  when f=100Hz, A=4V, and Offset=0V

Here we see the circuit wired up with wires connected for ground and measuring channels for the Analog Discovery.

Summary: The first graph shows a how current and voltage increase and decrease in the same time frame. The second graph's voltage and current graphs are more condensed than the first ones' due to higher frequency values. The third graph shows how linear increasing and decreasing of voltage results in flat lines for the current graph.

4-16: Passive RC Circuit Natural Response

Passive RC Circuit Natural Response

In this lab assignment, we examine the natural response of a simple RC circuit. First, we will find the natural response by opening a switch . Second by applying a switching step voltage from an arbitrary waveform generator . Lastly, we will simply short the voltage source to observe the response. 

 Here is a table of all the formulas related to resistors, capacitors, and inductors:

Pre-Lab: Following is the schematic of our RC circuit. We did calculated time constant since we were given R and C values. We estimated intital capacitor voltage and time constant for the circuit as shown below. 

Following is an image of oscilloscope window showing the capacitor voltage response for the circuit shown in previous image where V+ is used as the voltage source. 

Theoretical value for the  time constant is much samller than the experiment value time constant. Multimeter was not functioning correct at first that cause of error was big. 

The graph for part B:

 

For part B: Theoretical value for the  time constant is much close to  the experiment value time constant, but still have big error. 

Here is the voltage graph generated by the RL circuit:

Summary: In this lab, we have successfully learned the natural response of a simple, source free RC circuit. When a constant voltage apply to the circuit, the capacitor will only charged to whatever voltage we apply, and gives a really steep exponential voltage gain when the capacitor is begging charged, and a steep exponential voltage decay when the capacitor is being discharged. 

4-21: Inverting Differentiator

Inverting Differentiator

In this lab, we use an op amp (OP 27) and a capacitor to create an inverting differentiator. This means that the output voltage V_o is (a multiple of) the negative derivative of the input voltage V_in, or V_o = -RC*(dv_i/dt), where R is the feedback resistance, C is the capacitor capacitance, and v_i is the input voltage. If the input voltage v_i = Acos(ωt), where A is the input amplitude and ω is the angular frequency, then its derivative is (dv_i/dt) = -Aωcos(ωt). Thus the output voltage is V_o = RCAωsin(ωt).

 Here are the formulas related to the change of the voltage and current with time for capacitors, and inductors

Pre-Lab: We determine the Vo, V1, V3 ,use the data under.

When f=1kHz, A=1V, offset=0V, The display the waveforms for Vo A= 1.144V and Vin A=1V.

When f=500Hz, A=1V, offset=0V, The display the waveforms for Vo A= 0.586V and Vin A=1V.

When f=2kHz, A=1V, offset=0V, The display the waveforms for Vo A= 2.204V and Vin A=1V.

Theoretical value for the Vout  is much clossed to the experiment value. The min % different is 2.3% the max %different is 8.3%. 

 it has a  amplitude = 2.204V and the same pi/4 phase shit.

Summary: In this lab, we learned  the output voltage has a derivate with respect to the time of the input to the circuit relationship. With a higher frequency the the op amp will have a higher gain for the output, and with a lower frequency the op amp will have a lower gain for the input. 

4-28: Series RLC Circuit Step Response

Series RLC Circuit Step Response

Pre-Lab: Based on the characteristic equation, we can figure out the natural response of the RLC circuit. Alpha is defined as R/2L, and omega is defined as square root of 1/LC. The circuit is overdamped when alpha > omega, critically damped when alpha = omega, and underdamped when a < omega.

Theoretical value for the w, wd  is much clossed to the experiment value, but a has big error. 

This is the resulting output graph from the capacitor: We experimental alpha is 1.5*10^6, which is about172% of our theoretical alpha value of 550000. Possible source of error is from our input variables, the way we measured the circuit.


Summary: In this lab, we went over the basic principles of series RLC circuit, and did a lab to see how this type of circuit works when critically damped.