UIUC Physics 406
Acoustical Physics of Music
Resistor Measurements
We have developed a PC-based DAQ system that enables us to measure the complex impedance Z(f) = V(f)/I(f) of resistors.
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.
We then carry out a {0-C} least-squares fit to complex V(f), I(f), Z(f) and P(f) data which enables us to extract the
values of the inductance L(f), the AC series resistance in the inductive branch Rl(f), the {parallel} capacitance C(f)
and the series resistance in the capacitive branch Rc(f).
Metal-film (MF) resistors have Johnson (i.e. thermal) noise associated with them, whereas old-style carbon composition (CC) resistors
have 1/f noise associated with them in addition to Johnson noise. The use of CC resistors in tube amplifiers results in an audibly
"warmer" sound, whereas the use of metal film resistors sounds "cold" in comparison. Because of the underlying physics associated with
how electrons flow through the carbon-clay matrix of CC resistors, the moment-to-moment *fluctuations* in the resistance associated
with the 1/f noise component in CC resistors gives rise to moment-to-moment fluctuations in the signal - primarily phase noise -
giving rise to a scintillating "texture" to the sounds of the electric guitar output from a tube amplifier that uses CC resistors.
The human ear(s) are quite sensitive to *changes* in phase in the ~ 100 < f < ~ 1500 Hz frequency range.
Psycho-acoustically, humans prefer the subtle shimmering "detail" associated with the use of CC resistors in tube amplifiers,
as opposed to the cold, "lifeless" sound associated with MF resistors used in tube amps (which humans find "boring" in comparison,
and doesn't hold a person's attention nearly as long).
Return to the UIUC Physics 406 Experimental Results Page
Return to the UIUC Physics 406 EMI Sub-Webpage
Return to the UIUC Physics 406 Home Page