in which Julia learns about capacitors and investigates persistent wiggles
(I'm particularly excited about this because we just talked about modeling viscoelastic materials with an RC circuit in my Structural Biomaterials class!)Our first task: Lab 2-1 in H&H, in which we verify that a square wave applied to an RC circuit generates an asymmetrically peaked wave over the capacitor:
Image from Electronics pdf. |
Measuring the square wave (blue) and RC output (yellow). |
Next we used the LogoChip to characterize an RC circuit, building a "capacitance meter" wherein the LogoChip could read (and PicoBlocks could interpret) an unknown capacitance.
LogoChip RC circuit diagram (Electronics pdf). |
The real-life LogoChip RC circuit. |
PicoBlocks code for the LogoChip capacitor identification (Electronics pdf). |
(Δt) x 10^-6 s = R*C = (100 kΩ)*C = (1 x 10^5 Ω)*C
C = [(Δt) x 10^-3 s]/(1 x 10^5 Ω) = (Δt) x 10^-8 F = (Δt) x 10^-2 µF = C
The "capacitor meter" accurately identified both a 0.1 µF and a 1 µF capacitor by these calculations:
Identifying a capacitor based on the LogoChip/PicoBlocks output reading of 10. |
In further studies of the capacitance meter, we determined the effective capacitance of identical capacitors in parallel and in series. Recalling that capacitors in parallel add and capacitors in series add inversely, we were unsurprised to find that two parallel capacitors had double the effective capacitance of one, while two capacitors in series had half the capacitance. (PicoBlocks read 10 ms for one 0.1 µF capacitor, 20 ms for two caps in parallel, 5 ms for series.)
Finally we investigated the integrator circuit in Lab 2-3:
The integrating circuit: RC. |
In this circuit, the output voltage (Vout) is proportional to the charge on the capacitor, which in turn is proportional to the integral of the input voltage (Vin). With a square wave input, we expected the output voltage to appear as a triangle wave in the same phase, increasing when Vin was positive and decreasing when Vin was negative:
Our (correct) prediction for the integrator circuit output voltage (left) compared to the input voltage (right). |
Our experimental integrator, at high frequency (100 kHz) in good agreement with the prediction. |
A triangle wave input (purple) yields a cycloid output signal (yellow). |
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As expected, a sine wave input gave a cosine output. |
The input square wave (purple) was also correctly differentiated (yellow). |
The puzzling wiggle. |
The output wiggle after one calibration (yellow) suggests that we should replace the BNC breakout input cable (purple) with another scope probe. |
At last--a clear signal! |
Next lab: Impedence and Hi-Pass/Low-Pass Filters!
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