Inverting Differentiator

In addition to the lab, we conducted two exercises.

Derivation of the output of an integrator using ideal op amp properties and capacitor current

Evaluation of capacitor voltage subject to singularity function current

Diagram for differentiator circuit, including selected resistor and capacitor values, expected input and output functions (set equal to each other as shown, assuming unit amplitude), and derivation of ideal frequency for unity gain

Measured resistance. Capacitance measurement function non-operational, though measurement of time constant subject to square wave would be a viable option

Implemented circuit

Input (blue) and output (yellow) wave forms at 234 Hz, both of

amplitude 1V. 500Hz yielded output 2.1V and 100Hz 0.4V.

Summary

Circuit behaves as expected, yielding unity gain at the expected frequency and a phase shift of pi/4 consistent with cos differentiating to sin. Higher frequencies yield higher gain and low frequencies attenuation, as expected. Curiously, Waveforms' oscilloscope function refused to align the output with time 0 under any triggering configuration. Also, matte finishes are clearly superior to gloss.

Temperature Measurement System

In addition to the lab, we conducted three exercises.

First, we analyzed a cascaded op amp circuit consisting of two

non-inverting amplifiers, determining the resultant output

We also evaluated the relation of several input-output

configurations for a 3-bit digital analog converter circuit

In preparation for the lab, we derived the output of a

wheatstone bridge in which one resistor is allowed to vary

Proceeding with the lab, we produced a diagram for out temperature measurement circuit, in which a wheatstone bridge containing the thermistor supplies a difference amplifier. Given a desired minimum output swing and expected input variation, we derived necessary resistances for a consistent gain. Also shown are the measured values of the resistors used in our implementation

The implemented circuit

Collected data, including thermistor resistance seen by the bridge,

voltage supplied by the bridge, and output voltage of the amplifier

Video of the wheatstone bridge in operation

Video of the completed circuit in operation

Summary

The circuit behaved mostly as expected. The efficacy of the wheatstone bridge is difficult to judge, as biasing it is more fiddling calibration than direct implementation of theory. Nonetheless, we get output voltage ranging from 0 to 0.5, in line with expectations. We are let down, however, by the final output of the amplifier, falling short of the desired 2V range. Possible explanation for this could be input/output impedance between the bridge and amplifier. Regardless, it is a simple failure to rectify as the gain of the amplifier can be adjusted to yield desired results.

Difference Amplifier

In addition to lab, we conducted two exercises.

First, related to the lab, we derived the relation of input and output

voltages for a difference amplifier with nodal analysis

We also used nodal analysis to evaluate a nonstandard implementation of a difference amplifier

Proceeding to the lab, we determined resistances to use given constraints of input resistance and gain. Also shown here are the circuit diagram and first set of data. Resistor values were measured at 9.82k, 9.86k, 19.8k, 19.9k

The second data set

The implemented circuit

Plot of both data sets

Summary

 We see the expected results for the most part. va is subtracted from vb, yielding an output of their difference with a gain of 2. We again see saturation of the op amp, this time at different voltages: ~4.3V at the positive end and ~3.5V at the negative end, showing that the OP27 op amp does not necessarily supply evenly, nor all the way to its rail voltages.

Summing Amplifier

Before beginning the lab, we conducted two exercises.

First, the output of an inverting amplifier supplied by +5V and -0V with input of two square waves, with and without DC offset. In both cases we see the input amplified and reflected about zero, and in both cases the resulting negative component is clipped.

Second, we use nodal analysis to evaluate an ideal op amp circuit.

We then proceed to the lab, wherein we build a summing amplifier and supply it with two DC signals, one a constant 1V and the other ranging from -4V to +5V.

Circuit diagram with measured resistance values

Constructed circuit

Data (columns va, vb, vout) and comment

Summary

 We get results largely as expected for this circuit. All resistances equal, the two inputs are weighted equally in the sum and the op amp gives unity gain. Of note are the results of va=3V,5V, where the output is lower than expected, and the same value. This is presumably due to saturation of the op amp, and is consistent with there being two internal ~0.7V transistor voltage drops inherent to it.