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.

4-30: RLC Circuit Response

RLC Circuit Response

The purpose of this lab is to see the measured response of a second order circuit based on damping ratio and natural frequency. In this lab we are testing the step response and comparing the measured values to theoretical values that we derived from equations in class. These values include the damping ratio and natural frequency of the circuit.

We built the circuit with a 1.1Ω resistor, a 47 Ω resistor, a 10uF capacitor and a 1 uH inductor. 47 ohm resistor and the inductor are in series while they are in parallel with the other components in the circuit.

                                   

In the lab, the 47 ohm resistor has a real value of 49 ohm. The 1.1 ohm resistor has a real value of 4.3 ohm. The 10 uF capacitor has a real value of 9.92 uF, and we cannot measure the 1 uH inductor.  

We calculated our experimental value of α to be 3588.7, while our theoretical value is 1063.8. It has a precent difference of -237.4%. 

This is the input of our power. It is a square wave at frequency at 100 Hz, and amplitude of 2V at offset 0

Summary:

In this lab, we learn how to analyze circuits containing a resistor, capacitor and an inductor in parallel. There are three possible cases that may occur in a RLC circuit which include over damped, underdamped, or critically damped. Overall, we can see the relationship the circuits have in each other depending on the arrangement of the circuit and how this will affect the damping and natural frequency of the circuit.

5-07: Impedance

Impedance

In this lab we measured impedances of resistors, capacitors, and inductors. We then compared them to their expected values. The impedance of a resistor is just Z = R, so the impedance is really just the resistance of the resistor. For a capacitor, the impedance can be calculated as Z = 1/(jωC) , where j is the imaginary component, ω is the angular velocity of the input, and C is the capacitance of the capacitor. The impedance of an inductor is Z = jωL, where L is the inductance of the inductor. The phase angles for a resistor, capacitor, and inductor are 0°, -90°, and 90°, respectively.

The impedance and admittance of resistors, capacitors, and inductors.

Pre-Lab: We determined the resistor impedance = 47 + R , the real resistor values came out 48.7 ohm and 100.1 ohm, and therefore the expected impedance for resistors = 148.8 ohm  Inductor impedance = 48.7 + 0.00628j  Capacitor impedance = 48.7 - 1711.34j 

Output for circuit with input frequency of 1 KHz

part A: When frequencies are: 1kHz, 5kHz, 10kHz the V and i. And the time different is 0.

Output for circuit with input frequency of 5 KHz

Output for circuit with input frequency of 10 KHz

Part B: When frequencies are: 1kHz, 5kHz, 10kHz the V , i, time different  and z.

Output for circuit with input frequency of 1KHz

Output for circuit with input frequency of 5 KHz

Output for circuit with input frequency of 10 KHz

In the three graphs we see that the current lags the voltage by 90° as expected. Also, the voltage across the inductor increases as the frequency increases.

Part C: When frequencies are: 1kHz, 5kHz, 10kHz the V , i, time different  and z.

Summary: In this lab,  we went over impedance and admittance, and how to solve for them within circuits involving Resistors, Inductors, and Capacitors. We also did a lab to see how impedance works in real life.