Current Power Amplifier - Negative Resistance Amplifier

Negative resistance amplifier, except in some special occasions, the first one to be used in audio and succeeded was YAMAHA. Its main function is to improve the extension of low frequency, but it will have the effect of deteriorating the sound quality for frequencies above 200Hz, so it is generally used in ultra-low frequency active speakers.

In fact, this circuit is used in conjunction with speakers, and there is no practical significance for its use alone. Its working principle is: if the speaker is a rigid body, then adding a tube can become an ideal Holm's resonance box, then no matter how big the box is, how thick the tube is, as long as it meets the Holm's resonance calculation formula. Even the resonance point of 20Hz can be achieved, the size of the box is just the efficiency. Due to the existence of the speaker on the speaker, the speaker is moving when it sounds, and the speaker is not a rigid body, so the box will not produce Holm's resonance. Therefore, if the diaphragm of the speaker is stationary when it sounds. Then, the box is close to a rigid body, which can meet the conditions of Holm's resonance, and the resonance point of the box can be designed arbitrarily. The task of keeping the speaker still when sounding is the task of the negative resistance amplifier.

The working principle of negative resistance amplifier is that when the speaker works in the low frequency band, its impedance characteristics change sharply. The amplifier circuit takes out this change through current sampling and feeds it back to the amplifier, so that the amplifier controls the speaker in the form of current. If the amplifier circuit is analyzed equivalently, it can be found that the internal resistance of the amplifier is calculated as a negative resistance characteristic. During dynamic amplification, the internal resistance of the speaker plus the amplifier is close to 0. As a result, this circuit makes the speaker very damped no matter which direction it is facing. As long as the sound ends, the speaker will not move, and the box will become a rigid body. The so-called negative resistance is simply positive feedback.


The speaker discussed below is a direct radiation electric speaker, referred to as a direct speaker.

The direct speaker came out in 1924 and is known as the most beautiful invention of the 20th century. Although it has a history of more than 80 years, it still occupies a mainstream position in speakers and is known as a long-lived speaker. The reason why the direct speaker has been prosperous for a long time is that it has many advantages. However, it also has many defects. People have not made any breakthrough progress in improving it. Therefore, it is recognized as the weakest and most difficult link to improve in the entire chain of the electroacoustic system.

Existing electroacoustic systems all drive the direct-fire speakers with constant voltage, that is, they are driven by constant-voltage power amplifiers (abbreviated as amplifiers). Although the fidelity of current constant-voltage amplifiers has reached a near-ideal level, the direct-fire speakers driven by them are still far from ideal, resulting in the playback quality of the entire electroacoustic system being far from ideal.

Can we find a way to improve the playback quality of the electroacoustic system by changing the driving method of the direct-fire speakers? The answer is yes.


1.1 Basic theory

The direct-fire speaker is a complex electroacoustic device involving electricity, mechanics and acoustics. Now, take the direct-fire speaker mounted on an infinite baffle as an example to understand its input impedance ZY. ZY＝R＋jωL＋（Bl）2YM , R is the equivalent resistance of the voice coil of the direct-firing speaker; j is an imaginary unit, ω=2πf is the angular frequency of the sound signal, π is the circumference of the circle, f is the frequency of the sound signal, L is the equivalent inductance of the voice coil of the direct-firing speaker; B is the equivalent magnetic flux density in the magnetic gap of the direct-firing speaker, l is the equivalent total length of the voice coil wire of the direct-firing speaker in the magnetic field, YM=1/(RM+jωMM+1/jωCM) is the equivalent input force admittance of the vibration system and radiation load of the direct-firing speaker, RM=RM1+RMR1+RMR2 is the total equivalent force impedance of the direct-fire speaker mechanical system, RM1 is the equivalent force impedance of the direct-fire speaker vibrating body, RMR1 and RMR2 are the radiation force resistances on the front and back of the direct-fire speaker respectively, MM＝MM1＋MM2＋MMR1＋MMR2 is the total equivalent mass of the direct-fire speaker, MM1 is the equivalent mass of the cone of the direct-fire speaker, MM2 is the equivalent mass of the voice coil of the direct-fire speaker, MMR1 and MMR2 are the co-resonant masses on the front and back of the direct-fire speaker respectively, CM＝CM1CM2/（CM1＋CM2） is the total equivalent force compliance of the direct-fire speaker, CM1 is the equivalent force compliance of the yoke ring of the direct-fire speaker, CM2 is the equivalent force compliance of the center gasket of the direct-fire speaker, and (Bl)2YM is the motional impedance of the direct-fire speaker mechanical system.

After the mechanical system of the direct-radiation speaker is converted into circuit parameters, it is still a parallel resonant circuit, namely a current resonant circuit. Therefore, it presents high resistance at its parallel resonant frequency, namely the force resonant frequency fO, causing ZY to have the maximum modulus │ZY│MAX at fO; in the frequency band lower than fO, since the parallel resonant circuit is inductive, ZY is also inductive, that is, the modulus value of ZY │ZY│ decreases as f decreases; when f is higher than fO, the parallel resonant circuit is capacitive, and this capacitor resonates in series with the voice coil inductance L, namely voltage resonance, so it presents low resistance at its series resonant frequency, namely the electric resonant frequency fZ, causing ZY to have the minimum modulus value │ZY│MIN at fZ; when f is higher than fZ, the series resonant circuit is inductive, so ZY is also inductive, that is, the modulus value of ZY │ZY│ increases as f increases.

For closed and open boxes, i.e., direct-firing speakers on finite baffles, their │ZY│ frequency characteristics are the same as those of direct-firing speakers installed on infinite baffles, with only some specific details different; for direct-firing speakers installed on inverted boxes and other special sound boxes, their │ZY│ low-frequency characteristics are quite different from those of direct-firing speakers installed on infinite baffles. Due to space limitations, this article will not go into detail.

From YM＝1/（RM＋jωMM＋1/jωCM）, we can see that at fO, YM＝1/RM, so the quality factor of the direct-radiation loudspeaker mechanical system is QM 2＝MM /RM 2CM＝MMYM 2/CM, and the total quality factor of the electroacoustic system is QO2＝（RO＋R）2QM 2/（RO＋│ZY│MAX）2＝（RO＋R）2MMYM 2/（RO＋│ZY│MAX）2CM, from which we can get YM 2＝QO2（RO＋│ZY│MAX）2CM /（RO＋R）2MM, RO is the equivalent internal resistance of the sound power amplifier and its feeder. Since R, │ZY│MAX, MM, CM of the direct-radiation loudspeaker at fO are certain, its YM is only affected by QO and RO. It is not difficult to see that when QO is large, YM is also large; when QO is small, YM is also small.

When QO＞0.5, the direct-radiation speaker will oscillate, which will deteriorate the transient characteristics of the reproduced sound and increase the distortion. Only when QO≤0.5, the direct-radiation speaker will not oscillate. Therefore, when the reproduced sound is required to have good transient characteristics and small distortion, QO must be ≤0.5.

When QO＝0.5, the frequency characteristics of YM have the following characteristics: when f＜fO, YM∝f; when f＞fO, YM∝f－1.

It can be seen from ZY＝R＋jωL＋（Bl）2YM that at fO, because L can be ignored, ZY＝R＋（Bl）2YM. And because YM 2＝QO2（RO＋│ZY│MAX）2CM /（RO＋R）2MM at fO, it is obtained that ZY 2＝R2＋（Bl）4QO2（RO＋│ZY│MAX）2CM /（RO＋R）2MM at fO. Obviously, │ZY│ at fO is also affected by QO and RO. It is not difficult to see that when QO is large, │ZY│ is also large; when QO is small, │ZY│ is also small.

When QO＝0.5, the frequency characteristics of │ZY│ have the following characteristics: when f＜fO, │ZY│∝f ; when fO＜f＜fZ, │ZY│∝f－1; when f＞fZ, │ZY│∝f . For a non-inductive direct-radiation speaker with a voice coil inductance L of 0, │ZY│∝f 0, that is, │ZY│ is basically constant.

For a sound wave with a plane wavefront, the wavefront area S does not change with the propagation distance r. If the loss of sound wave energy by the medium is ignored, the instantaneous value of sound pressure p and the instantaneous value of particle velocity v do not change with the propagation distance r. The wavefront area S, the instantaneous value of sound pressure p and the instantaneous value of particle velocity v in the sound wave equation and the wave equation are no longer functions of the propagation distance r. Therefore, the ratio of the complex value of sound pressure P at a certain point in the sound field of a simple harmonic plane sound wave to the complex value of particle velocity V at the same point is the wave impedance ratio ZS＝P/V＝ρOCO. ρO is the static density of the medium, and CO is the speed of sound in an infinitely large uniform medium.

For a sound wave with a spherical wavefront, the wavefront area S will change with the distance r from the measuring point to the equivalent center of the sound source, that is, S = 4πr2, so the wave impedance modulus of the simple harmonic spherical sound wave │ZS│2＝P2 / V2＝ρO 2 CO 2（kr）2 /［1＋（kr）2］. Obviously, the │ZS│ of the simple harmonic spherical sound wave is related to kr. When the distance r is far and the sound wave frequency f is high, that is, kr＞10, the impedance in the spherical sound wave │ZS│ is so small as to be negligible compared with the resistance, so it can be treated as a plane sound wave, that is, ZS＝P/V ≈ρOCO . k＝ω/CO＝2π/λ is the wave number, and λ＝CO / f is the wavelength of the sound wave.

The radiator of a direct-fire speaker can be approximately regarded as a piston radiator, so the sound pressure of a direct-fire speaker can be calculated by using the sound pressure expression of a circular piston in simple harmonic vibration on an infinite baffle in the far field, that is, P(θ) = ρOCO ka2VJ1(ka·sinθ)/r(ka·sinθ), P(θ) is the sound pressure at a point r from the geometric center of the piston at an angle θ to the normal of the piston surface, a is the radius of the radiation surface of the direct-fire speaker, and J1(ka·sinθ) is the first-order cylindrical function with (ka·sinθ) as the variable, that is, the Bessel function. It can be seen that the sound pressure P of a sound wave of a certain frequency in space is not only a function of the direction angle θ and ka, but also decreases linearly with the increase of the distance r. This shows that the far-field sound waves radiated by the direct-fire speaker are not completely spherical waves, and the sound pressure P at different points on its spherical wavefront is different, which is caused by θ and ka.

It can be seen from the directivity coefficient of the piston radiator DS (θ) = 2J 1 (ka·sinθ) / (ka·sinθ) that the smaller ka is, the wider the directivity is; the larger ka is, the narrower the directivity is. When ka is large to a certain extent, secondary directivity will also appear. This shows that the sound energy radiated by the direct-fire speaker is concentrated in the normal direction of the piston surface. Therefore, if the radiated sound pressure in the normal direction of the piston surface has a flat frequency response, the sound pressure frequency response at other angles will produce a linear distortion of high-frequency decline, and this distortion will increase with the increase of ka. Since secondary directivity appears when ka is large, the sound pressure frequency response of the direct-fire speaker radiator in the non-normal direction will show a "comb-like" characteristic when ka is large. This fully shows that the high-frequency sound waves of the direct-fire speaker are close to plane waves, so they can be treated as plane waves.

Although when kr>10, spherical waves can be approximately treated as plane waves, because the actual listening and calculation distance r of the direct-fire speaker cannot be too far, it cannot be treated as a plane wave at low frequencies. In the normal direction of the direct-radiation speaker radiator, that is, when θ = 0°, J1 (ka·sinθ) / (ka·sinθ) = 1/2, so the complex sound pressure value P = ρOSfV/r. S = πa2 is the effective radiation area of ​​the direct-radiation speaker.

1.2 Constant voltage drive

In order to reduce the calculation error of P, it is assumed that when f < fZ, P = ρOSfV/r, that is, it is treated as a spherical wave; when f > fZ, P = ρOCOV, that is, it is treated as a plane wave. In addition, according to Ohm's law of mechanics, V = FYM, F is the electric force acting on the direct-radiation speaker radiator. According to the electrodynamic principle, F = BlI, I is the driving current of the direct-radiation speaker. According to Ohm's law of electricity, I = U/ZY, U is the driving voltage of the direct-radiation speaker. Therefore, the sound pressure expression of the constant pressure drive of the direct-radiation speaker is: when f＜fZ, P＝ρOSfBlUYM/rZY; when f＞fZ, P＝ρOCOBlUYM/ZY.

When f＜fZ, because ρO, S, B, l, U, r are constant, P∝fYM/ZY; when f＞fZ, because ρO, CO, B, l, U are constant, P∝YM/ZY. When f＝fO, because YM2＝QO2（RO＋│ZY│MAX）2CM/（RO＋R）2MM, ZY2＝R2＋（Bl）4QO2（RO＋│ZY│MAX）2CM/（RO＋R）2MM. Therefore f 2YM 2＝fO 2 QO 2（RO＋│ZY│MAX）2CM /（RO＋R）2MM , P2∝fO 2 QO 2（RO＋│ZY│MAX）2CM /（RO＋R）2MM /［R2＋（Bl）4QO&nbs