# Measuring Amplifier Damping Factor with APx500

Created on 2009-08-21 02:21:00

The Damping Factor of an amplifier is defined as the ratio of its rated load impedance to its output (source) impedance. In loudspeaker systems, the damping factor is considered to be a measure of the amplifier’s ability to control undesirable movement of the speaker cone near the resonant frequency of the speaker system.

Damping factor can easily be calculated by measuring an amplifier’s output voltage with and without its rated load impedance attached (typically 4 Ω or 8 Ω). Consider the loaded and unloaded circuits below, where RO represents the amplifier’s output impedance, RL represents its rated load impedance, VNL is the voltage measured with no load, and VL is the voltage measured under load. Note that for the purposes of this measurement, RO is assumed to be totally resistive, and RL is a non-inductive load resistor.

##### Schematic of test setup.

The load resistance acts as a voltage divider, such that

…………………………………………… (1)

The above equation can be rearranged to yield

…………………………………………… (2)

But by definition, the damping factor (DF) is equal to RL / RO. So, we can determine the damping factor directly from the measured voltages as

………………………………………………. (3)

The amplifier’s output impedance can vary with frequency, and therefore it may be desirable to measure damping factor as a function of frequency. This can be done by conducting sweeps of the loaded and unloaded amplifier circuit and applying the damping factor equation at each step in the sweep.

When making connections, note that both the speaker cable to the dummy load and the measurement cable to the analyzer must be connected directly to the speaker terminals of the DUT. This Kelvin-type connection renders any speaker cable resistance insignificant by adding it to the load.

##### Damping factor test setup, with measurement correctly made at the speaker terminals.

If the measurement is taken at the load instead of at the speaker terminals, then the speaker cable resistance and amplifier output impedance (both typically 0.2 Ω or less) get added together and large measurement errors can result.

### APx Damping Factor Measurement Utility

Audio Precision has developed a utility for conducting damping factor measurements with an APx500 Series audio analyzer. The utility was developed in LabVIEW 8.6, and is available as LabVIEW source code for users who have a LabVIEW development system, or as a compiled application for those who don’t. The source code and the compiled application are designed to work with APx500 version 2.4. To install the application, unzip the installer and run the setup program. The installer places a shortcut on the desktop as well as in the Start menu.

When the utility is started (Figure 1), it opens the APx500 software if it isn’t already running. If a project file has been loaded, it displays the name. It also enumerates the APx500 project and gets lists of all the Signal Paths and Measurements in the project. A damping factor measurement can be based on any of the measurements used to conduct a level versus frequency measurement, (i.e. Frequency Response, Continuous Sweep, Stepped Frequency Sweep, or Multitone Analyzer) except for Acoustic Response. A button is included on the front panel to allow you to load an APx500 project file, if required.

To run a damping factor measurement, use the controls provided to select the Signal Path and Measurement to be used for the test. By default, these controls are set to the first Signal Path in the project and the first Frequency Response measurement in that path (if one exists). Then click the Run Damping Factor Test button.

##### Figure 1. The APx Damping Factor Measurement Utility.

The utility will first prompt you to disconnect the load from the amplifier (Figure 2). Once the OK button is clicked, it conducts the specified level versus frequency measurement on the unloaded amplifier.

##### Figure 2. Instructions for Part 1.

Next, the utility prompts you to connect the amplifier load (Figure 3). As noted, at this point the units should not be changed, the graph should not be re-sized, and auto scaling should be disabled. Clicking OK will run the test again on the loaded amplifier.

##### Figure 3. Instructions for Part 2.

Once Part 2 is complete, the utility calculates the damping factor using equation (3) and plots the results on the graph (Figure 4). It displays results for each of the analog input channels enabled in the APx software. As shown, it also retrieves the channel labels from the system (in this case, “Left” and “Right”).

##### Figure 4. Damping factor measurement results.

For a hard copy of the damping factor results, click the Print Results button. This opens a Print Results dialog window (Figure 5), which includes various test details and a note field where you can add an annotation, if desired. Click the Print button to print this results window to the system default printer.

##### Figure 5. Print dialog.

The Export Data button allows you to save the data in tab-delimited text format, which can be opened by typical spreadsheet programs like Microsoft Excel. Figure 6 shows the data after the text file has been opened in Excel.