Project: Analog Synthesizer

Project assembly began on 5/26 with a first attempt at the sawtooth oscillator. Upon lack of oscillation, the diodes were checked and found to be rectifier diodes rather than switching

diodes. The subcircuit would be left until the proper diodes arrived in the mail.

Assembly proceeded on 6/2, the ordered parts having arrived. We constructed the sawtooth and

wien bridge oscillators and found neither to yet be properly functional. We were, however, able

to properly drive the constructed voltage controlled resistor, for which we determined the ideal controlling voltage range for output resistance by experimental iteration.

Assembly and testing proceeded, the sawtooth oscillator becoming functional by 6/7. A buffer amplifier and current sourcing transistor were added at the output in an effort to clean up the rather distorted output as well as to properly supply the speaker, from which we were unable to get sound.

By 6/8 we had determined that the oscillation criterion for the wien bridge oscillator was too sensitive to vary the frequency with a single pot, and we resorted to static paired resistors, the intention being to switch between them with dpdt switches.

After significant tinkering and some mystery, we were not only able to get sound out of our speaker, but the sawtooth wave had cleaned up into a perfect ramp function with the transistor found to be unnecessary. The keyboard was constructed, tuned, and integrated into the sawtooth oscillator, the VCR integrated into an amplifier final stage (filtering found to be ineffective, an alternative was found in ADDING distortion rather than filtering it out), and a switch added to permit toggling between sawtooth and the alternate pulse train output. Voltage supply issues unfortunately precluded the use of the wien bridge oscillator, and LFO was instead provided by the analog discovery. We then varied the LFO settings looking for a desirable timbre, and found only one in ramping the "filter" in a manner characteristic of much electronic dance music. Assembly was completed by gluing stubborn switches in place and wrapping the entire assembly in bubble wrap to give some durability.

Passive RL Filter

Circuit diagram with calculated voltage gain and cutoff frequency

Implemented circuit, oscilloscope measuring both resistor and inductor voltages

Measured resistor and inductor voltages at various frequencies.

Complete data

Summary

The circuit behaves as expected. The two voltages cross at the half-power gain and at the cutoff frequency. The shape of the frequency dependence is consistent with the bode plot we expect of a high pass filter.

Signals with Multiple Frequency Components

Circuit diagram, calculation of expected gain for three experimental frequencies.

Implemented circuit, oscilloscope measuring across capacitor resistor parallel combination.

Measured composite input voltage and output voltage.

Voltage under frequency sweep.

Summary

Circuit behaves mostly as expected. The frequency sweep clearly shows greater attenuation at higher frequency as expected of a low pass filter. Curiously, while the lower two frequencies of the composite wave form were attenuated near as expected, the high frequency component appears to have been amplified. This is inconsistent with a low pass filter and something for which we don't have an explanation.

Phasors: Passive RL Circuit Response

Before proceeding to the lab, we did a number of exercises with phasors and phasor arithmetic.

Circuit diagram with calculation of cutoff frequency and voltage gain for a number of frequencies.

Implemented circuit, analog discovery connected to measure input voltage and inductor voltage.

Measured input and output voltage and calculated current at 470krad/s

Summary

Calculating gains as Vo/Vi and reading phase angles from oscilloscope output, then comparing to theoretical gain and phase angle arctan(w L / R), we find errors of less than 5% for gain in all frequencies tested. Phase angles, however, had errors of 10-20%. Overall, our theoretical expectations are largely consistent with the practical implementation.

Thevenin's Theorem

A number of exercises on Thevenin equivalents accompanied the lab,

in addition to a brief treatment of Norton equivalents.

Circuit diagram and calculation of Thevenin Equivalent.

Implemented circuit, multi-meter configured to measure the Thevenin equivalent voltage and, with the sources short circuited, resistance

Circuit reconfigured with potentiometer as load resistor, multi-meter measuring pot resistance.

Table of measured load resistances and voltages.

Plot of power vs load resistance, calculated as V^2/R

Summary

We find Thevenin's Theorem to be accurate, the theoretical equivalent voltage and resistance matching the measured values within 1%. Additionally, we find some support for maximum power being obtained when load resistance is equal to the Thevenin resistance. While more data points are necessary to properly confirm, the form of the data appears to be quadratic with a peak in the neighborhood of the Thevenin resistance.

Superposition

Before the lab, we did a number of exercises including

mesh analysis with dependent sources and linearity

Circuit diagram including both sources. Below are calculated voltages

on the left and measured voltages on the right.

The implemented circuit, multi-meter configured to measure total voltage with both sources in place.

Summary

The results of this experiment are not satisfactory to confirm the validity of the superposition principle. While the measured total voltage differs from the theoretical by a mere 10%, the single source voltages are of concern. Firstly, they are each in error of 50%. Worse, they do not add to the total measured voltage, the error there being 36%. In conclusion, we see that the total voltage calculated via superposition is correct within reasonable error, but that the singe source voltages are wildly inaccurate. This is likely the result of mistakes in the implementation of the circuit or the supplies.

Nodal Analysis

Circuit diagram and calculation of expected voltages via nodal analysis.

Implemented circuit, multi-meter configured to measure V2.

Multi-meter configured to measure V1

Beginning exercises in mesh analysis followed the lab.

Summary

While the theoretical values are uncertain (there was quite some variation across the class), the measured values appear to support nodal analysis as an effective means of evaluating the function of a circuit. There is some error, which may be attributed to variation in resistance values or mistakes in the implementation of the circuit, such as reversed supplies, none of which were verified at the time of the experiment.