Final Project: The Marx Generator

The Marx generator is a voltage multiplying device. It's purpose is similar to that of the Cockroft-Walton generator but the main difference is that the Marx generator periodically unleashes a high voltage pulse as opposed to the high-voltage, constant DC from the Cockroft-Walton generator.

Marx Generator

Our primary goal for this project was to be able to observe and measure a spark length of about 30 kV (that's roughly a 1 cm spark) at the output of the Marx generator. The theoretical output is said to be equivalent to nV, the number of stages multiplied by the input voltage.

The Marx generator is designed such that it charges in parallel along the consecutive rows of resistors and discharges in series through the diagonal spark gaps.

In order to observe sparks in our generator, we needed to look for a constant, high-voltage source. We were advised to use a transformer from an electric flyswatter. Fortunately, we were able to find an inexpensive swatter at Walmart for $7.

We removed the transformer inside the flyswatter which looked like this:

We built a mini version of the Marx generator on a breadboard and ran it through our transformer (whose voltage was rated at 1780 V on a DMM)

The generator ran pretty well! We got about 5 to 6 mm on the generator which meant we were on track considering there may be practical discrepancies. 

We continued building until we reached 16 stages and measured the spark gap. Sure enough, we got our 1 cm spark gap. 

To put things in perspective, the breakdown voltage in air at 1 cm are:

Theoretical	Experimental
30,000 V	28,480 V

As a bonus, our result had an error margin of 5.07%.

Bill of Materials

• Electric flyswatter - $7.00
• 40 x 1 MΩ, 0.5 W resistors - $8.00
• 1 x 6.25 MΩ resistor $0.20
• 20 x 1 nF, 3000 V capacitors $6.00
• Breadboards (2) - $20.00
• Alligator clips - $5.00

          Total: $46.20

Criteria for Success

• Ensure we get a spark of 1 cm
• The experimental result is reasonably consistent with the theoretical output, nV, within 10% of theoretical value
• Sparks go across the entire stages of the Marx generator

Powerpoint link:

<iframe src="http://www.slideshare.net/slideshow/embed_code/22934113" width="427" height="356" frameborder="0" marginwidth="0" marginheight="0" scrolling="no" style="border:1px solid #CCC;border-width:1px 1px 0;margin-bottom:5px" allowfullscreen webkitallowfullscreen mozallowfullscreen> </iframe> <div style="margin-bottom:5px"> <strong> <a href="http://www.slideshare.net/alvintung33/ppt-22934113" title="Ppt" target="_blank">Ppt</a> </strong> from <strong><a href="http://www.slideshare.net/alvintung33" target="_blank">Alvin Tung</a></strong> </div>

MOSFET Controlled Electric Motor

The experiment was to use a MOSFET transistor connected to a potentiometer to make a speed controller.

 The design looked like the following:

We successfully built the speed controller whose speed varied as we turned the potentiometer:

FreeMat 2

The second FreeMat assignment dealt with the use of phase angles in sinusoidal waves.

Adding Sinusoids

The result of adding two sinusoids

Assignment 1

1. Two circuits with the output 2e^(-t/τ) with two different time constants. The circuit with the smaller time constant will have the lowest output sooner.

2. The output is now 2(1-e^(-t/τ)).

Assignment 2

1. Determine the output when adding 3 sin(2t + 10) and 5 cos(2t-30)

2. For a large number of frequencies.

Operational Amplifiers II

The second part of the op-amp experiment is to observe the changing of input and feedback resistors. We began by setting up the inverting amplifier

If the fixed input resistor is 10 kΩ, then we need a 100 kΩ resistor to achieve a gain of -10.

If V_sen = 1 V, the current leaving the op-amp is I_OP = 0.1 mA.

We constructed the following setup and made measurements

Vin Desired	Vin Actual	Vout Measured	VRF Measured	IOP Calculated	ICC Measured	IEE Measured
0.25 V	0.248 V	-2.48 V	2.48 V	0.0248 mA
0.5 V	0.5 V	-4.81 V	4.83 V	0.05 mA
1.0 V	1 V	-10.03 V	9.95 V	0.1 mA	0.889 mA	-0.982 mA

Kirchhoff's Current Law is confirmed when we add I_CC and I_EE to yield I_OP.

The power supplied by the 12 V supplies were

P_CC = (12 V) (I_CC) = (12 V) (0.889 mA) = 10.67 mW

P_EE = (12 V) (I_EE) = (12 V) (0.889 mA) = 11.78 mW

We added a 1 kΩ resistor to the output shown below

and measured the following

Vin Desired	Vout Measured	VRF Measured	IOP Calculated	ICC Measured	IEE Measured
1.0 V	-9.97 V	9.75 V	0.1 mA	0.887 mA	-0.987 mA

We can see that KCL is obeyed when we sum I_CC and I_EE.

Again, we calculated the power:

P_CC = 10.64 mW

P_EE = 11.84 mW

Extra Credit

In order to achieve a gain of -5 in our inverting amplifier, our value for the feedback resistor must be 50 kΩ.

Our measurements were:

Vin Desired	Vout Measured	VRF Measured	IOP Calculated	ICC Measured	IEE Measured
1.0 V	-5.04 V	4.98 V	0.1 mA	0.885 mA	-0.985 mA

The behavior of the circuit is exactly the same as the two previous measurements made in the experiment.

Second Order Circuit Tutorial

This serves as acknowledgement that we completed the second order circuit assignment. The results of each question is posted below:

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Capacitor Charging/Discharging

The experiment was to design a charge/discharge network using capacitors and resistors in series. The design required us to find a way to charge the capacitor in 20s, then abruptly discharging it in 2s. With a few calculations, our design was built in the following manner:

We determined the values of the capacitor, charge resistor, and discharge resistor to be 47 µF, 85 kΩ, and 8.5 kΩ, respectively. We ran the circuit through a 9 V power supply, charged the capacitor by closing the left half of the circuit and discharged it by immediately closing the right half. and recorded the data on Logger Pro. Our results were:

As expected, the capacitor charges at 20 s and discharges in 2 s. 

Follow-up Questions

1. During charging,

    R­_Th = R_charge * R_leak / (R_charge + R_leak)

           = 85 kΩ * 992.5 kΩ / (85 kΩ + 992.5 kΩ)
           = 78.3 kΩ

2. During discharging,

    R­_Th = R_discharge * R_leak / (R_discharge + R_leak)
           = 8.5 kΩ * 992.5 kΩ / (8.5 kΩ + 992.5 kΩ)
           = 8.4 kΩ

3. When V = 0.6321 * (final voltage), τ_c = 4.0 s. Thus, R = τ_c / C = 85.11 kΩ
    The value is indeed close to the value in question 1.

Practical Questions

1. C = 2E / V² 
        = 2 * 160 MJ / (15 kV)2
        = 1.42 F

2. If the capacitance is arranged in the schematic, the value of each capacitor, C, is 0.71 F

Oscilloscope 101

This exercise was to familiarize ourselves with the use of the oscilloscope and to study and adjust different waveforms on the frequency generator.

Exercise 1
We began by displaying a simple sinusoid on the oscilloscope with the following setup:

According to the scope,

The period was at 208 microseconds.

Peak-to-peak amplitude was 10 V.

Zero-to-peak amplitude was 5 V.

Anticipated RMS value was 3.54 V.

We measured the VDC and VAC RMS values and got the following:

VDC = 6.2 mV

VAC = 2.34 V

The  VAC value was close to our anticipated RMS value.

Exercise 2

The next exercise was to add a 5 V offset to the existing waveform.

We measured the DC and AC voltage with the DMM.

VDC = 5.35 V
VAC = 2.45 V

Exercise 3
We measured the DC and AC voltages.

VDC = 5.2 V
VAC = 5.13 V

The expected VAC value for a square wave is 5 V, which is similar to the value we measured with the DMM.

Mystery Signals
We were given an unknown signal generated by the frequency generator and attempted to trigger on the signal. However, the limitations of the oscilloscope prevented us from fully triggering on the signal. The output is as follows:

The signal was a triangle pulse with the following:

DC voltage: 0.5 V 

Frequency: 7 Hz

Pk-pk Amp: 1 V