Additional Specifications of Power Amplifiers

The list of additional specifications of power amplifiers can be endless. However, we will mention here some of them which are more important.

Damping Factor

A flat frequency response is desirable to avoid tonal coloration, but a flat response may not always be obtained when the amplifier is driving a real-world loudspeaker load. The input impedance of real loudspeakers can vary dramatically as a function of frequency, while the output impedance of the power amplifier is nonzero. A voltage divider is thus formed by the amplifier output impedance and the loudspeaker input impedance. Here the amplifier is modeled with an ideal amplifier with zero output impedance in series with impedance Zout that describes its actual output impedance (referred to as a Thévénin equivalent circuit). This is where the damping factor (DF) comes into play. In spite of its important-sounding name, this is just a different way of expressing the output impedance of the amplifier.
While amplifiers ideally act like voltage sources with zero output impedance, they all have finite output impedance. The term damping factor came from the fact that a loudspeaker is a mechanically resonant system; the low output impedance of an amplifier damps that resonance via the resistance of the loudspeaker’s voice coil and electromotive force. An amplifier with higher output impedance will provide less damping of the loudspeaker cone motion because it adds to the total amount of resistance in the circuit. Damping factor is defined as the ratio of 8 Ω to the actual output impedance of the amplifier. Thus, an amplifier with an output impedance of 0.2 Ω will have a DF of 40.
Most vacuum tube amplifiers have a DF of less than 20, while many solid-state amplifiers have a DF in excess of 100. It is important to bear in mind that the DF is usually a function of frequency, often being larger at low frequencies. This is consistent with the need to dampen the cone motion of woofers, but ignores the influence of the DF on frequency response at higher frequencies. Many loudspeakers have a substantial peak or dip in their impedance at or near their crossover frequencies. This could result in coloration if the amplifier DF is low.
The effect of damping factor and output impedance on frequency response must not be underestimated in light of the large impedance variations seen in many contemporary loudspeakers. It is not unusual for a loudspeaker’s impedance to dip as low as 3 Ω and rise as high as 40 Ω across the audio band. Consider this wildly varying load against the 0.4 Ω output impedance of a vacuum tube amplifier with a DF of 20. This will cause an audible peak-to-peak frequency response variation of ± 0.5 dB across the audio band.

Dynamic Headroom

Unlike a sine wave, music is impulsive and dynamic. Its power peaks are often many times its average power. This ratio is often referred to as the crest factor. Dynamic headroom refers to the fact that an amplifier can usually put out a greater short-term burst of power than it can on a continuous basis. The primary cause of this is power supply sag which is a reflection of power supply regulation. The power supply voltages will initially remain high and near their no-load values for a brief period of time during heavy loading due to the energy storage of the large reservoir capacitors. Under long-term conditions, the voltage will sag and less maximum power will be available. Consider an amplifier that clips at 100 W into 8 Ω on a continuous test basis. If this amplifier has a power supply with 10% regulation from no-load to full load (which is fairly good), the available power supply voltage will be about 10% higher during a short-term burst. This will result in a short-term power capability on the order of 120 W, since power goes as the square of voltage.
Dynamic headroom is a two-edged sword. It is good to have it because music tends to have an average power level much lower than the brief peak power levels it can demand (referring again to the crest factor). It is nice to have 20% to 40% more power available when it is needed for those brief peaks. On the other hand, a large amount of dynamic headroom is often symptomatic of an amplifier with a sloppy power supply.

Slew Rate

Slew rate is a measure of how fast the output voltage of the amplifier can change under large-signal conditions. It is specified in volts per microsecond. Slew rate is an indicator of how well an amplifier can respond to high-level transient program content. A less capable amplifier might have a slew rate of 5 V/µs, whereas a really high-performance amplifier might have a slew rate on the order of 50 to 300 V/µs. For a given type of program material, a higher-power amplifier needs to have a higher slew rate to do as well as a lower-power amplifier, since its voltage swings will be larger. A 100-W amplifier driving a loudspeaker whose efficiency is 85 dB will need to have 3.16 times the amount of slew rate capability as a 10-W amplifier driving a 95 dB speaker to the same sound pressure level.
As a point of reference, the maximum voltage rate of change of a 20 kHz sine wave is 0.125 V/µs per volt peak. This means that a 100-W amplifier that produces a level of 40 V peak at 20 kHz must have a slew rate of at least 5 V/µs. In practice a much larger value is desirable for low-distortion performance on high-frequency program content. Although technically imprecise, the rate of change of a signal is often referred to its slew rate for convenience.
The slew rate capability of audio power amplifiers received a lot more attention after the term transient inter-modulation distortion (TIM) was coined and studied intensely during the 1970s and early 1980s. This was largely another way of describing high-frequency distortion that resulted from slew rate deficiency.

Output Voltage and Current

Here we will briefly touch on the reality of output voltage and current swing that an amplifier may have to deliver in practice. The first table on Picture 1 shows the RMS value of the sine wave voltage, the peak voltage, the peak current, and the reserve current required for the popular 8 Ω resistive load as a function of power. The reserve current listed below is simply a factor of three greater than the peak current required of a resistive load and represents the reality of driving difficult reactive loudspeaker loads with non-sinusoidal wave forms. The reserve current can be assumed to occur only in a brief time interval under fairly rare circumstances.

Picture 1: Voltage and Current into a 8, 4 and 2 Ω Load


This data gives a glimpse of what is necessary for the amplifier to provide. Notice the very substantial voltage swings, and implied power supply voltages, required for a 400 W amplifier. The peak and reserve currents are also into the tens of amperes at 400 W. This is just the beginning of the story, however. The second table shows what the same amplifier would encounter when driving a 4 Ω load. Here we have assumed that the drive signal has remained the same and only the load impedance has dropped. We have also implicitly assumed that the amplifier has ideal power supply regulation, so all of the power numbers are doubled.
Given the nature of some of today’s high-end loudspeakers, some have argued that really high-performance amplifiers should be rated for power delivery into 2 Ω (at least for short intervals). Indeed, the testing done in some amplifier technical reviews regularly subjects power amplifiers to a 2 Ω resistive load test. The figures for output current become almost bewildering under these conditions. An important point here is that there are amplifiers sold every day that are rated at up to 400 W per channel into 8 Ω, and designers implement such amplifiers every day.
The sobering point is that if at the same time the designer thinks in terms of his amplifier being 2 Ω compatible, the potential demanded burst current could on occasion be quite enormous. This is illustrated in third table shown on Picture 1.