UIUC Physics 406
Acoustical Physics of Music
Capacitor Measurements

We have developed a PC-based DAQ system that enables us to measure the complex impedance Z(f) = V(f)/I(f) of capacitors. A PC talks to an Agilent 33220A function generator via GPIB (General Purpose Instrumentation Bus) controlling its frequency (nominally 5 Hz to 20.005 KHz in 10 Hz steps) and voltage amplitude (nominally 1.0 volt). The sine-wave signal from the function generator (a near-ideal voltage source, 50 Ohm output impedance) is converted to a near-ideal constant current source, simply by sending the signal through a 1.5 meg-ohm metal film resistor. The sinusoidal signal after the 1.5 M resistor is connected to the electric guitar pickup. A 100 Ohm metal film resistor is connected in series with the pickup on the ground side. The voltage across the pickup and current flowing through the pickup (measured as a voltage developed across the 100 Ohm resistor in series with the pickup) are first buffered by low-noise, unity-gain precision instrumentation op-amps (AD624's), the voltage signals of which are input to SRS830 DSP lock-in amplifiers. We record the in-phase ("real") and 90-degrees out-of-phase ("imaginary"/quadrature) components of the complex voltage V(f) and current I(f) output from the SRS830 DSP lock-in amplifiers {both of which are phase-referenced to the sinusoidal signal output from the function generator}. Four 12-bit ADC's (Analog-to-Digital Converters) on a National Instruments LabPC+ DAQ card are used to digitize the in-phase and 90-degrees out-of-phase signals output from the two lock-in amplifiers: Re(V), Im(V), Re(I), Im(I). We then compute, on-line (and off-line) the magnitudes and phases of the voltage and current, |V| and |I|, and phi_V and phi_I respectively. We also compute, on-line (and off-line), the in-phase, 90-degrees out-of-phase components, and magnitude and phase of the complex impedance Z(f) = V(f)/I(f), i.e. Re(Z), Im(Z), |Z| and phi_Z at each frequency, f as well as those parameters associated with the complex electrical power {P(f) = V(f)I*(f)}, i.e. Re(P), Im(P), |P| and phi_P at each frequency, f.

Modern capacitors (e.g. Sprague/Vishay "Orange-Drop" metallized polypropylene film capacitors) have considerably lower losses/dissipation associated with their dielectric materials than "vintage" capacitors (e.g. Astrons, Bumblebees, Black Cats, Yellow Jackets, Packtrons,...) made in the 50's and 60's. We show here some of the results we have obtained for various of these capacitors.

• [1a] Complex V(f), I(f), Z(f), P(f) for 0.1 uF 600 V Sprague 715P Orange Drop Cap.

• [1b] Step-Function Voltage Response vs. time for {modern} 0.1 uF 600 V Sprague 715P Orange Drop Cap.

• [2a] Complex V(f), I(f), Z(f), P(f) for 0.1 uF 600 V Bumblebee Cap (the type of capacitor e.g. as Used in Gibson Les Pauls made in the 1950's).

• [2b] Step-Function Voltage Response vs. time for 0.1 uF 600 V Bumblebee Cap.

• [3a] Complex V(f), I(f), Z(f), P(f) for 0.05 uF 600 V Astron Cap (the type of capacitor e.g. as used in Fender "tweed-era" amps made in the 1950's.

• [3b] Step-Function Voltage Response vs. time for 0.05 uF 600 V Astron Cap.

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