Power amplifier parameters (Part 1)

It has been more than 120 years since Edison invented the phonograph in 1877. From the mechanical recording/playback system to the current high-tech digital system, the progress has been earth-shaking. However, the development of audio technology in the past 120 years has been very uneven. In the approximately 60 to 80 years after the invention of the phonograph, the development of audio technology was quite slow, but it also achieved certain results, such as the replacement of mechanical recording and playback with electric recording and playback, and the beginning of the use of multi-pole vacuum tubes.

The rapid development of audio technology was in 1927, when Bell Laboratories in the United States announced the epoch-making negative feedback (NFB) technology, and audio amplifiers entered a new era. The origin of the so-called high-fidelity amplifier should be traced back to the Williamson amplifier published in 1947. At that time, Mr. Williamson introduced a tube amplifier circuit that successfully used negative feedback technology to reduce distortion to 0.5% in an article on the design of Hi Fi amplifiers. The sound quality was unprecedented at the time and quickly became popular all over the world, becoming an important milestone in the history of Hi Fi. Four years after the Williamson amplifier was launched, in 1951, the American Audio magazine published an article on "Super Linear Amplifier". In June of the following year, another circuit design combining the Williamson amplifier with the super linear amplifier was published. Because the super linear design greatly reduced nonlinear distortion, many people followed suit, forming a craze again. The influence of ultra-linear design still exists today in the 21st century. It can be said that Williamson amplifiers and ultra-linear amplifiers marked the maturity of negative feedback technology in audio technology. Since then, amplifier designs and types have flourished. The progress of technology is beyond the reach of the previous 70 years.

The specifications of an amplifier are an important indicator of its performance. Of course, another important indicator is to listen to it. I often hear audiophiles say that the specifications of audio equipment are meaningless. Many amplifiers with excellent test data have terrible sound. This is only half right. First of all, these excellent data are generally obtained when testing prototypes during the product development stage. In the mass production stage, its performance will generally be discounted to a certain extent, depending on the grade of the equipment. Secondly, although current technology has greatly improved the performance of amplifiers, it is extremely difficult to amplify 20~20KHz audio signals without distortion that the human ear cannot detect. Moreover, the so-called performance specifications of general amplifiers only give a few data, most of which are only measured under certain physical conditions. It is not enough to reflect the basic performance of the amplifier.

There are two methods for evaluating the technical specifications of amplifiers: dynamic and static. Static specifications refer to the indicators measured by sine waves in steady state. This is actually a frequency analysis method in Classical Control Theory. It has been used since the 1920s and 1930s. Test items include frequency response, harmonic distortion, signal-to-noise ratio, intermodulation distortion and damping coefficient. Dynamic specifications refer to the indicators measured by more complex signals such as square waves and narrow pulses, including phase distortion, transient response and transient intermodulation distortion. Dynamic testing is actually similar to the transient response test commonly used in industrial automatic control systems, except that industrial testing often uses step signals, while audio testing uses shortened step signals - square waves. To generally reflect the quality of the amplifier, dynamic testing and data must be considered comprehensively. As for human ear audition, since it contains more subjective factors, it is not intended to be discussed in detail here. Since most manufacturers only provide a few parameters for their products, the author would like to take this opportunity to introduce some of the more important specifications of audio equipment to help new audiophiles and some non-engineering personnel have a deeper understanding of audio technology.

Frequency Response

Among many technical indicators, frequency response is the most familiar specification. For some amplifiers, it is theoretically sufficient to achieve a flat frequency response of 200,000 to 20,000 cycles, but the overtones (harmonics) contained in real music may exceed this range. In addition, in order to improve the performance of transient response, the amplifier is required to have a higher frequency response range, such as from 10 Hz to 100 kHz. The customary regulation of the frequency response range is: when the output level drops by 3 decibels at a certain low frequency point, the point is the lower limit frequency, and when it drops by 3 decibels at a certain high frequency point, it is set as the upper limit frequency. This decibel point has another name, called the half power point (Half Power Point). Because when the power drops by half, the level drops by exactly 1 decibel. One thing that must be pointed out is that although the half power point has a certain meaning for some electronic equipment and automatic control systems, it may not be suitable for audio equipment, because the human ear can resolve sound up to 0.1 decibels. Therefore, some high-end equipment is rated at 20 to 20K and can reach plus or minus 0.1 decibels. In fact, the nominal specification of 10 to 50K + 3DB may be higher. By the way, there are actually two frequency response curves, which are called "Bode Plots" in control engineering. The amplitude-frequency curve is the common frequency response graph we often see, and the other is called the phase-frequency curve, which is used to indicate the degree of phase distortion (phase distortion) produced by different frequencies after passing through the amplifier. Phase distortion refers to the time difference (phase difference) generated by the signal from the input end to the output end of the amplifier. The smaller this time difference is, the better, otherwise it will affect the operation of the negative feedback circuit. In addition, phase distortion is also related to transient response, especially the transient to modulation distortion that has received increasing attention in recent years. For Hi Fi amplifiers, phase distortion must be at least within the range of 20~20KHz+-5%.

Harmonic distortion

Any natural physical system will generally experience a periodic vibration with attenuation after being disturbed by the outside world. For example, if a half-meter-long string with fixed ends is plucked in the middle, a vibration wave with a wavelength of 1 meter will be generated, which is called the fundamental wave. In addition to swinging greatly along the center point, the string itself also makes many small vibrations that are difficult to detect with the naked eye. The frequency is generally higher than the fundamental wave, and there is more than one frequency. Its size and type are determined by the physical properties of the string. In physics, these vibration waves are called harmonics. For the sake of convenience, the harmonic waves generated by musical instruments are often called overtones. In addition to being generated by the signal source, harmonics can also be generated when the vibration wave encounters an obstacle during propagation and produces reflection, diffraction and refraction.

Both the fundamental wave and the harmonics are "pure" sine waves (Note: Sine waves are periodic functions, consisting of positive half cycles and negative half cycles, but the negative half cycle can never be called a negative sine wave!), but when they are combined together, they will produce many strange waveforms. Figure 3: A waveform composed of a fundamental wave plus a second harmonic (twice the frequency and half the amplitude). The square wave that everyone is familiar with is composed of a sine wave fundamental wave plus a large number of single-order (odd) harmonics, which also explains why square waves are often used as test signals.

The amplifier circuit is full of various electronic parts, wiring and solder joints, which can more or less reduce the linear performance of the amplifier. When the music signal passes through the amplifier, the nonlinear characteristics will cause the music signal to be distorted to a certain extent. According to the above theory, this is equivalent to adding some harmonics to the signal, so this signal distortion is called harmonic distortion. It is not difficult to understand why harmonic distortion is often expressed as a percentage. A small percentage means that the amplifier produces fewer harmonics, which means that the signal waveform is less distorted. The harmonics generated by different physical systems have different components. But they all have one thing in common, that is, the higher the frequency of the harmonic, the smaller its amplitude. Therefore, for audio amplifiers, the two to three harmonic distortion components with frequencies closest to the fundamental wave that cause obvious audible distortion in the sound are.

When manufacturers calibrate the harmonic distortion of their products, they usually only give one data point, such as 0.1%. However, the harmonics generated by the amplifier are not a constant, but a function related to the signal frequency and output power. Figure 4 shows the relationship between the harmonic distortion and signal frequency of two typical transistor dual-channel amplifiers. Figure 5 is the relationship between the harmonic distortion and output power of a transistor amplifier with an output of 100W. As can be seen from the figure, when the output power approaches the maximum value, the harmonic distortion increases sharply. This is because the transistor will clip when it is close to overload. It is obviously a serious waveform distortion to cut off the top of a signal. Harmonic distortion will naturally increase significantly.

Harmonic distortion is not completely useless. One of the reasons why the sound of tube amplifiers is soft and beautiful is that they mainly produce even harmonic distortion. That is, harmonics with frequencies 2, 4, 6, 8, ... times the fundamental frequency. Because the harmonic level is inversely proportional to the frequency, the second harmonic has a large amplitude and a large impact, while the others have a small amplitude and a large impact, and the others have a small amplitude and a slight impact. Although the second harmonic is technically a distortion, its frequency is one times the fundamental wave, which is exactly an octave, that is, it forms a pure octave with the fundamental wave in music. We know that the pure octave is the most harmonious and beautiful harmony. So it is not difficult to understand why tube amplifiers sound sweet and rich in musicality. In the 1940s, many "smaller" radios deliberately added a considerable degree of second harmonic distortion. The purpose was to create "heavy bass" to please consumers. The sound can be very enjoyable, but it is completely contrary to the requirements of high fidelity.

Signal-to-Noise Ratio

Signal-to-noise ratio (SNR) is abbreviated as SNR or SNR, which refers to the ratio of useful signal power to useless noise power. It is usually measured in dB. Since power is a function of current and voltage, SNR can also be calculated using voltage values, that is, the ratio of signal level to noise level, but the calculation formula is slightly different. Calculating SNR by power: S/N=10 log Calculating SNR by voltage: S/N=10 log Since SNR is logarithmically related to power or voltage, to improve SNR, the ratio of output value to noise value must be greatly increased. For example, when the SNR is 100dB, the output voltage is 10,000 times the noise voltage. For electronic circuits, this is not an easy task.

If an amplifier has a high signal-to-noise ratio, it means that the background is quiet. Due to the low noise level, many weak sound details that are covered by noise will appear, increasing floating sounds, strengthening the sense of air, and expanding the dynamic range. There is no strict judgment data to measure whether the signal-to-noise ratio of an amplifier is good or bad. Generally speaking, it is better to be above about 85dB. If it is lower than this value, it is possible to hear obvious noise in the gaps of music in some high-volume listening situations. In addition to the signal-to-noise ratio, the concept of noise level can also be used to measure the noise level of the amplifier. This is actually a signal-to-noise ratio value calculated using voltage, but the denominator is a fixed number: 0.775V, and the numerator is the noise voltage, so the difference between the noise level and the signal-to-noise ratio is: the former is an absolute value, and the latter is a relative number.

In many product manuals, there is often an A behind the data in the specification table, which means A-weight. Weighting means that a certain value has been modified according to certain rules. Since the human ear is particularly sensitive to the intermediate frequency, if the signal-to-noise ratio of an amplifier in the intermediate frequency band is large enough, then even if the signal-to-noise ratio is slightly lower in the low and high frequency bands, it is not easy for the human ear to detect it. It can be seen that if the weighted method is used to measure the signal-to-noise ratio, its value will definitely be higher than that without the weighted method. For A-weighting, its value will be about decibels higher than that without weighting.

Intermodulation Distortion

As the name implies, intermodulation distortion refers to the distortion caused by mutual modulation of signals. The term modulation originally refers to a technology used in communication technology to improve the efficiency of signal transmission. Because the original signal containing sound, image, text, etc. is "added" to the high-frequency signal, and then the comrades send out this synthesized signal. This process and method of "adding" high and low frequencies is called modulation technology, and the synthesized signal is called a modulated signal. In addition to retaining the main characteristics of the high-frequency signal, the modulated signal also contains all the information of the low-frequency signal. The process of generating intermodulation distortion is actually a modulation process. Since an electronic circuit or an amplifier cannot achieve completely ideal linearity, when signals of different frequencies enter the amplifier at the same time and are amplified, under the action of nonlinearity, each signal of different frequencies will automatically add and subtract, generating two additional signals that are not in the original signal. If the original signal has three different frequencies, there will be 6 additional signals. When the original signal is N, the output signal will be N (N-1). It is conceivable that when the input signal is a complex multi-frequency signal, such as an orchestral instrument, the amount of additional signals generated by intermodulation distortion is staggering!

Since intermodulation distortion signals are all sums and differences of musical frequencies, exactly the same as natural sounds, the human ear is sensitive to them. Unfortunately, in many amplifiers, intermodulation distortion is often greater than harmonic distortion, partly because harmonic distortion is generally easier to deal with.

Although intermodulation distortion and harmonic distortion are both caused by the nonlinearity of the amplifier, and from a mathematical point of view, both add some additional frequency components to the positive signal, they are actually different. Simply put, harmonic distortion is the distortion of the original signal waveform, which can occur even when a single frequency signal passes through the amplifier circuit, while intermodulation distortion is the mutual interference and influence between different frequencies. Measuring intermodulation distortion is much more complicated than measuring harmonic distortion, and there is no unified standard yet.