DIY Vacuum Tube Amplifiers
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Measuring Amplifier Damping Factor
The following procedure requires a digital AC meter that reads in true RMS values. However, meters that read at average AC values (a digital multimeter, for instance) can be fairly accurate as long as the AC signal is low distortion and a lower frequency such as 100 Hz.
For the safety of the amplifier under test, measurements should be taken at a power output level of about 1−watt. This should be a safe level for most amplifiers, solid state or vacuum tubes. For low-power amplifiers, testing with a lower power output test level may be prudent.
Required Resources
The following is required to perform measurements. An AC digital meter as mentioned. A low distortion 100 Hz signal
source. And, an 8−ohm power load resistor measured with a digital ohm meter to find its actual resistance.
Finding The Source Impedance:
→Connect a 100 Hz test signal to the amplifier input. There should be no load connected to the amplifier speaker
output.
→With a digital AC meter connected across the amplifier's speaker output, and the amplifier's input level at minimum
volume, turn on the amplifier and allow a suitable warm-up time. Increase the input volume level until the AC meter reads
about 3.0 volts and write down the exact voltage reading on paper.
→Without making any adjustments, with the AC volt meter still connected to the amplifier output, connect the
8−ohm load resistor across the speaker output along with the AC voltmeter. Write down the exact AC voltage reading
on paper.
→Subtract the loaded AC voltage reading from the no-load AC voltage reading. Then divide the result by the loaded
AC voltage reading.
→Using the actual measured resistance of the 8−ohm load resistor, multiply the value from the previous
calculation by the measured value of the load resistor.
For instance, if the load resistor measures 8.1 ohms, and the no-load AC value is 3.1 volts, with a loaded AC voltage value of 3.0 volts, then the source impedance would be 0.27 ohms.
The Damping Factor is the load resistance divided by the source impedance. In this example, 8.1 / 0.27 = 30.
The source impedance is also known as the output impedance.
What Is Amplifier Damping?
Cone/voice coil speakers are subject to overshoot and decayed vibration by the cone suspension damping effect. When a signal is applied to the speaker's voice coil, then removed, the speaker's cone suspension overshoots as it pulls the cone back to its center position. The result is extra air molecules being vibrated that, to some degree, create an effect altering the original sound. It is an undesirable effect and can change the sound of certain instruments, in particular percussion and bass instruments.
This overshoot effect can be controlled by limiting voice coil travel. The voice coil works by the audio signal interaction with a magnet in the speaker frame. When the audio signal stops, the cone suspension pulls the cone back to its center position. During travel back to center position, the magnets magnetic flux cuts through the voice coil generating a 'back electromotive force' (back EMF). The power amplifier driving the speaker can reduce speaker overshoot if its output has an impedance low enough to load down and counter the back emf.
Although a power amplifier has an 8−ohm speaker output impedance, it also has a source impedance. An amplifier's source impedance is an AC property that behaves or reacts when handling dynamic audio in a way that results in an impedance much lower than the speaker output impedance. In a vacuum tube power amplifier, If you measure the DC resistance of an output transformers secondary 8−ohm output, you will measure about one ohm, perhaps 0.8 ohms. Although that is a fairly low resistance, its impedance to frequencies is not low enough to offer any apprecable oppisition to the low impedance of a speaker voice coil. If the amplifier includes negative feedback from the output stage back to a predeeding voltage amplifier stage, any back EMF from the speaker is amplified providing a damping counter voltage by a factor based on the amount of negative feedback. In effect, the amplifiers source impedance is reduced to a lower impedance than the amplifiers speaker 8−ohm output DC resistance. The amplifiers source impedance dampens or reduces the speakers overshoot.
Negative feedback lowers the source impedance, increasing the amplifier's damping factor. This gives the amplifier tighter control over the speaker cone, improving transient response. Negative feedback should be kept to a reasonable level. There is really no need for triple digit damping factors. Speaker cables and any resistance between the amplifier and speakers, including connectors, lowers the 'system' damping factor, effectively rendering ultra-high amplifier damping specs moot.
For DIY amplifier designs, besides real world damping factors being in the lower two-digit range, consider problems associated with ultra-high negative feedback. Pushing negative feedback too far without proper phase-compensated design can cause high-frequency phase shifts. This can result in circuit instability including self-oscillation. Amplifier circuits that lack sufficient open-loop speed or high-frequency headroom, extreme feedback can trigger transient intermodulation (TIM) distortion when overloaded,
How Much Damping?
Source: Dick Pierce Paper
Date: 1998-2002
The process of amplifier damping is explained with analysis on levels of damping factor. The following are brief excerpts from the paper. Mr. Pierce's area of expertise was in professional audio development.
In his introduction, Mr. Pierce states that much ballyhoo surrounds the concept of "damping factor." It's been suggested that it accounts for the alleged "dramatic differences" in sound between tube and solid-state amplifiers. Also, many of the claims made, especially for the need for triple-digit damping factors, are not based in any reality, be it theoretical, engineering, or acoustical.
What is the damping factor? Simply stated, it is the ratio between the nominal load impedance (typically 8 ohms) and the source impedance of the amplifier. Note that all modern amplifiers (with some rare exceptions) are, essentially, voltage sources whose output impedance is very low. That means their output voltage is independent over a wide range of load impedance.
Mr. Pierce ran an analysis of the effects of amplifier damping factor on the decay time and frequency-dependent response of a closed-box, acoustic suspension loudspeaker system. The results were that any damping factor over 10 resulted in inaudible differences.
The paper written by Mr. Pierce is technical, detailed, and contains related formulas. The paper may be difficult to
follow. If interested, a PDF of the original paper is available
here.
EJ Jurich
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Any circuits or project information presented on ejjurich.com has been tested for safe operation. Vacuum tubes get hot. Amplifiers with exposed vacuum tubes should be operated out of reach of children. Project assembly usually involves fabrication with tools and the use of a hot soldering iron. It is up to the project builder to insure the safety of everyone involved, including curious onlookers. EJ Jurich and ejjurich.com assumes no responsibility for damage, injury or otherwise related to any use of information on this site or given by other means. Many electronic circuits, in particular vacuum tube circuits, operate with dangerous voltage and current. Always exercise care when working with electronic circuits.