Notes from the Test Bench

By Bruce Hofer, Chairman & Co-Founder, Audio Precision

We're all looking forward to NAB in Las Vegas and AES in Amsterdam. Both shows promise to deliver as AP introduces new products and Technotes to help you get your job done faster and easier. I hope to see many of you at one or both of the shows.

In the meanwhile, our Director of Engineering Thomas Kite has put together a very interesting article on measuring complex impedance, and one of AP's earliest employees, John Payne, goes through a Factory Adjustment. Hopefully it will serve as a reminder to everyone of the importance of keeping instruments regularly serviced.

Finally, those of you who subscribe to the AES Journal will see AP's new ad in the March issue. For those who don't have access to the Journal, the ad is reposted on the AP website here. The ad's point is simple: words come cheap and the proof is in the measurements. It's a value that I hold very closely, and one that drives every decision we make at AP. As a loyal AP user, I'm sure you will agree as well.

Bruce

Output: Tech tips and new applications from AP

Measuring complex impedance with SYS-2722

Director of Engineering Thomas Kite looks at the math involved in calculating complex impedance with the SYS-2722. Includes an AP Basic macro available for download.

Linear passive circuit elements are characterized by their impedance. Impedance is a complex quantity consisting of a real part, known as the resistance, and an imaginary part, known as the reactance. The reactance is frequency dependent and can take two forms: inductive, in which the voltage waveform leads the current waveform, and capacitive, in which the voltage lags the current. Since impedance is frequency dependent, a variable frequency generator and AC level and phase meters are required to measure it. This makes the SYS-2722 ideal for making audio-frequency impedance measurements.

This article shows how to make impedance measurements using SYS-2722, a test jig, and a supplied macro. The jig can be simply cables and a fixed resistor; AP tech support equipped a project box with connectors to make the job easier. The macro presents a user interface to set the measurement parameters. The results are shown in graphical form in the software.

Test Setup

Here,  Rfixed is a fixed resistor of known resistance, Z is the impedance under test (IUT), and  Zin is the input impedance of the SYS-2722 analog input. As the frequency of the generator is varied, the frequency dependence of the IUT causes the measured level at input B and the measured phase between input B and input A to vary. This allows Z to be computed at each frequency.

Circuit diagram of the test jig

Derivation of impedance

From the circuit above, using the potential divider equation, we see that

V_b / V_a = Z_tot / (Z_tot + R_fixed )                      (1)

where V_a and V_b are the complex levels at inputs A and B respectively, R_fixed is the known test resistance, and Z_tot is the parallel combination of Z and Z_in. Therefore

Z_tot = R_fixed (V_b / V_a) / (1-V_b / V_a) .

We also know that

Z_tot = Z · Z_in / (Z + Z_in)

And therefore we arrive at

Z =Z_in · Z_tot / (Z_in - Z_tot ) .                           (2)

Calibrating Z_in

The unbalanced input of the SYS-2722 has an impedance of 100 kOhm in parallel with 185 pF. However, the test jig and cables used to connect the fixed resistor and the IUT may add to this. In particular, long cables are likely to add capacitance comparable to the input capacitance of the SYS-2722. For accurate measurements, it is necessary to account for this extra capacitance.

The macro in this article provides a calibration cycle for this purpose. When performing a calibration cycle, the IUT must be removed from the circuit, leaving the jig and cables otherwise untouched. Once the calibration has been performed, the IUT is returned to the jig and the measurement is made. If the jig is not changed, the code can be updated with the measured value of the input impedance, so a further calibration cycle is not needed.

Complex numbers

Because impedance is a complex quantity, we need complex mathematics to compute it. In equation (1) above, V_a, V_b, and Z_tot  are all complex quantities. To use a SYS-2722 to measure complex impedance, we need to tackle two problems:

1. SYS-2722 does not natively return complex values for measured levels.
2. AP Basic does not natively calculate with complex values.

Polar vs. rectangular representation

SYS-2722 has a level meter for each input channel, and a phase meter that measures the phase difference between input A and input B. If the generator signal is fed to input A, then the phase meter measures the phase of input B relative to the generator. This gives us a magnitude-phase, or polar, representation of the signal on input B. This can be converted to a complex value with the identity

V_b= V cos(ø) + jV sin(ø)

where V_b is the complex voltage at input B, V is the measured level on input B, ø is the phase meter reading in radians, and j= √-1. This is known as a rectangular representation. It is entirely equivalent to the polar representation, but is preferred here because it is easier to perform complex math in the rectangular representation.

Complex math in AP Basic

AP Basic calculates using real arithmetic. Special code must be written to perform complex arithmetic. This article uses a small library, Complex.lib, to handle complex numbers. The library defines a new data type as follows:

Type Complex
     re As Double
     im As Double
End Type

A constructor allows a new Complex to be created, and math functions take Complex parameters and produce Complex results. For example:

Function Times(a As Complex, b As Complex) As Complex
     Times.re = a.re * b.re - a.im * b.im
     Times.im = a.re * b.im + a.im * b.re
End Function

Two complex numbers can then be created and multiplied with the following code:

Dim a As Complex, b As Complex, c As Complex
a = Complex(1, 2)
b = Complex(3, 4)
c = Times(a, b)

giving the complex result in c (c.re = –5, c.im = 10). AP Basic does not provide fully object-oriented classes and operator overloading, so code that makes use of the Complex library can be difficult to read at first.

Supplied macros

The easiest way to get started with impedance measurement is to use the supplied macro Impedance UI.apb. This macro was written by Audio Precision technical support, and presents a user interface to allow impedance measurements to be made easily. It also interacts with the Windows registry to store settings like the measured input impedance of your 2722.

Impedance UI.apb interacts with Impedance.apb. This macro contains the core functions which calculate the IUT impedance and the instrument input impedance from measured sweep data.
A ‘#Uses Impedance.apb statement should be included if you want to make use of these functions in your own code.

Impedance example.apb also uses the functions in Impedance.apb, but does not present a user interface. This macro is provided to show how to use these functions in your own code.

Using the macros

Both Impedance UI.apb and Impedance example.apb calculate the impedance of the IUT by running a sweep over the audio frequency range, measuring the channel A level, channel B level, and phase at each point. They then call Impedance.apb, which applies equations (1) and (2) above at each frequency to calculate the IUT impedance. The following figures are calculated and graphed:

• Impedance magnitude (Ohms)
• Impedance phase (degrees)
• Resistance (Ohms)

The code can easily be changed to plot other commonly used parameters such as reactance, admittance (reciprocal of impedance), conductance (reciprocal of resistance), or susceptance (reciprocal of reactance).

Some measured results

Downloads

• Complex Impedance AP Basic macros (includes PDF of this article)

Reference

• “Agilent Technologies Impedance Measurement Handbook”, July 2006, Agilent Technologies. Retrieved from http://cp.literature.agilent.com/litweb/pdf/5950-3000.pdf.

Sound Advice: Audio Test Q&A

Well Adjusted

Tom Williams interviews AP’s Service Supervisor John Payne as he performs a Factory Adjust on a SYS-2712 audio analyzer. John has been with AP almost since the company began in 1984. There is very little he doesn’t know about audio analyzers.

Q: Why should AP customers get an adjustment?
The short answer is more accurate measurements. All high precision instruments drift to some degree: we have to send our scopes and other equipment out to Tek and Agilent to get adjusted, and it’s the same for AP gear. We also install ECOs when the instrument is back at the Factory, so in fact, you can end up with an instrument that’s even better than before.

Q: What do the ECOs do?
The Engineers are constantly working on ways to improve performance, even on older instrument families, plus certain components go End of Life, and we need to find alternatives. Engineering Change Orders let the Service Department know what updates to install on analyzers when they come in for service.

Q: Why don’t customers adjust their own instruments?
There are lots of reasons, but basically it comes down to time, expertise, and equipment. We get a lot of units sent to us by independent Calibration Houses who have no idea how to adjust our analyzers. They’re complicated instruments. We also have some software that we’ve developed in-house over the years that speeds up the process. The other big consideration is that if a repair is necessary, it saves the customer a lot of time if the instrument is here already. We can just repair it and get back on the customer’s bench where it belongs.

Q: What should customers do before they send in their units?
Call us first! Customers have to get a RMA before sending in their units. Other than that, we recommend running a Performance Check before sending in your unit. It gives our technicians an idea of where to look if there are any issues, and it gives the customer a reference of the state of the instrument before it was shipped.

Q: Thank you for your time John. Any last comments?
There is more hand-selection of parts for the 2700 than I’ve ever seen in my 35 years of electronics. It’s truly a hand-crafted instrument.

AP’s Service Supervisor John Payne at his bench

John Payne with his trusty Coilcraft tweak tool and voltmeter characterization table

Test Results: AP News & Events

UPCOMING EVENTS

NAB Show 2008 | Las Vegas
April 14-17
AP's booth is N6125 in Hall N-3
Visit the show website

AES Europe 2008 | Amsterdam
May 17-20
Visit the show website

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