Abstract:
This disclosure shows methods and apparatus to emulate vacuum tube amplifiers that have output transformers, to deliver “tube sound”, where the output transformer nonlinearity is emulated. Prior arts that emulated vacuum tube amplifiers either did not include output transformer nonlinearity in their emulation, or did not do it correctly. The disclosed methods and apparatus have the advantage of low cost and flexibility, because the output transformers are included in the emulation.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    This invention is in general related to audio systems, and in particular related to methods and apparatus to alter audio signals to produce the type of soft and euphonic sound typically produced by vacuum tube amplifiers. 
         [0003]    2. Brief Description of the Related Prior Art 
         [0004]    The first group of prior arts are vacuum tube amplifiers, which include high-end audio amplifier and music instrument amplifiers. The second group of prior arts are circuits invented by people to mimic the “tube sound” with solid state equipments. The third group of prior arts are circuits invented by people to protect loudspeaker cones from over excursion. 
         [0005]    It has long been claimed by some audiophils and musicians that tube amplifiers sound better than solid-state amplifiers. The sound produced by tube amplifiers are described as “clean”, “soft”, “smooth”, “fat”, “detailed”, “enphonic”, “life like”,“vivid”, etc. It is sometimes described as “tube sound”. People developed theories to explain the causes of tube sound. Some representative publications are, “The Cool Sound of Tubes”, Spectrum, IEEE, August 1998; “Tubes Versus Transistors: Is There an Audible Differences?” by Russell O. Hamm, Journal of the Audio Engineering Society, May 1973, Volume 21, Number 4, page 267-273; “Tubes verses transistors in electric guitar amplifiers”, W. Stephen Bussey, IEEE International Conference on ICASSP &#39;81. April 1981, Volume: 6, page 800-803. 
         [0006]    I published a paper “Why Do Tube Amplifiers Have Fat Sound while Solid State Amplifiers Don&#39;t”, Audio Engineering Society Convention 131, Oct. 20-23, 2011, New York, Paper Number:8536. It is referred as “my AES paper” in this application. In that paper, I found that the frequency dependent transformer nonlinear distortion may contribute to the tube sound. In said paper, I described flowcharts on how to emulate tube amplifiers with circuits without the output transformer. 
         [0007]    Beyond the tube amplifiers themselves, there are other prior arts related to producing the tube sound. I describe some of them as follows. 
         [0008]    In U.S. Pat. No. 5,802,182, Prichard teaches a method to emulate the output transformer. He observed that output transformer selectively attenuate low frequency signals while leave high frequency signals almost untouched. With his method, When both low frequency signals and high frequency signals are applied separately, his method can softly clip low frequency signal and leave the high frequency signal largely untouched. However, when the two kind of signals are applied together, the soft clipping of the low frequency signal affects the superposed high frequency signal, introducing unwanted intermodulation. 
         [0009]    In US patent application US2004/0070438A1, Ohshima pointed out such a problem of conventional limiter. Though Prichard&#39;s distortion means is “soft” other than “hard” as the conventional limiter that Ohshima wanted to fix, it had similar problem as large amplitude low frequency soft clipping will affect the high frequency signal. 
         [0010]    In U.S. Pat. No. 4,113,983, Steel teaches a way to limit the amplitude of movement of the loudspeaker cone. He used a variable high frequency filter. He used a threshold means to determine whether there is a need to raise the breakpoint frequency of the high frequency filter. When there is a need, he rapidly increase the breakpoint frequency so low frequency frequency will be attenuated more; while there is no need, he slowly decrease the breakpoint frequency to the rest frequency. 
         [0011]    In U.S. Pat. No. 4,327,250, Von Rechlinghausen teaches a way to protect the loudspeaker from damaging. He used filter, rectifier-smoother and a threshold to detect whether there is a need to modify the signal to prevent loudspeakers from damaging. 
         [0012]    In US patent application US2005/0207584, Bright tought 
         [0013]    In U.S. Pat. No. 5,481,617, Bjerre re-arranged Von Rechlinghausen&#39;s circuit, basically combine the variable high-pass filter and the low-pass control filter to make a band-pass filter, and added a high-pass filter to undo the low-pass control filter to produce the output. He removed the smoother to make the response instantaneous. 
         [0014]    In U.S. Pat. No. 5,528,695 ( FIG. 7 ) Klippel used a linear filter which follows the loudspeaker characteristic, followed by an envelop detector to generate control signal which anticipate the signal peak. The control signal is smoothed by a leakage integrator which have a short time constant for the attack slope and a long time constant for the decay to avoid audible modulation of the audio signals by the control signal. If the peak exceeds a threshold, the input signal is attenuated to prevent loudspeaker overload. He has both feed-forward and feed-back configurations. 
         [0015]    In U.S. Pat. No. 5,577,126 ( FIG. 8 ), Klippel used a linear filter H X  to monitor the loudspeaker load, and if the load exceed a threshold, the controller C will activate the feedback loop to attenuate the input signal. Note that the control signal is again smoothed by a leakage integrator which have a short time constant for the attack slope and a long time constant for the decay to avoid audible modulation of the audio signals by the control signal. 
         [0016]    In US patent application US2005/021573 A1 ( FIG. 10 ), Poletti uses a feedback system to control the bandwidth of an amplifier according to the level of the input signal. He required the filter H(s) to have at least a low pass filter, so it looks like his purpose was to change the bandwidth from the up side of the audible bandwidth. However, if the filter H(s) also have a high pass filter component, as one of his examples shows, the system is capable to attenuate the low frequency signal too. This makes his patent closely related to Kohut&#39;s patent. One difference is where the output signal is taken. In Poletti&#39;s patent the output signal is after the filter H(s), while in Kohut&#39;s patent the output signal is combined from signals taken both before and after the filter. The parameters of the filter H(s) need to be different too. 
       BRIEF SUMMARY OF THE INVENTION 
       [0017]    It is well known that transformer core saturation causes distortion for low frequency audio signals. It is little known that this distortion probably is the cause of the “clean”, “soft” or “smooth” property of the tube sound. 
         [0018]    It is known that the speaker cone excursion is reversely proportional to signal frequency. Referring to said my AES paper, it is clear that a typical tube amplifier acts like a frequency selective nonlinear feedback system that softly limits the speaker cone excursion for low frequency music signal with excessive amplitude, but has little effect on high frequency music signal or low frequency music signal with low to moderate amplitude. Better yet, at least for one direction of the signal polarity, when low frequency music signal with excessive amplitude is superposed with high frequency music signal, tube amplifiers selectively limit low frequency music signal and has little effect on the high frequency music signal. 
         [0019]    Upon studying the tube amplifier, I come up with simple models of tube amplifiers, including models of output transformers, which is readily implemented without having to use bulky out put transformers found in typical vacuum tube amplifiers. 
         [0020]    People have long come up with inventions to softly limit the excursion of speaker cones. The prior arts described are just some representative ones. However, because those prior arts were not derived from emulating a real vacuum tube amplifier, there are important difference between the present invention and the prior arts. One important one is that the present invention has a feedback paths for both the voltage and current of the speakers while the prior arts don&#39;t. One other difference is that with the prior arts, the quality of the sound produced by speakers are unknown. With the present invention, one can have a real vacuum tube amplifier measured, the vacuum tube nonlinearity and transformer iron core nonlinearity modelled, and an emulator constructed to precisely reproduce the sound of the real vacuum tube amplifier. The method of modelling is disclosed in said my AES paper. Further more, some drawbacks associated with real vacuum tube amplifiers can be remedied in the emulator. For example, hum can be completely removed from the emulator. New nonlinearity models that are not yet existing in vacuum tubes or transformer core irons can be introduced into the emulator, to produce audio effects that is not yet exploited with existing vacuum tube amplifiers. 
         [0021]    The object of the present invention is to provide novel methods and apparatus to emulate a vacuum tube amplifier, without having to use output transformers. 
         [0022]    Since the current invention has the capability to softly limit the excursion of speaker cones, it has the effect of protecting speakers from damages caused by excessive cone excursion. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0023]      FIG. 1  illustrates a typical single ended triode amplifier, according to the prior art. 
           [0024]      FIG. 2  illustrates Pritchard&#39;s transformer emulator, according to the prior art. 
           [0025]      FIG. 3  illustrates Bright&#39;s loudspeaker displacement limiter, according to the prior art. 
           [0026]      FIG. 4  illustrates Holman&#39;s loudspeaker protector, according to the prior art. 
           [0027]      FIG. 5  illustrates Steel&#39;s filtering apparatus for loudspeakers, according to the prior art. 
           [0028]      FIG. 6  illustrates Von Recklinghausen&#39;s dynamic loudspeaker equalizer, according to the prior art. 
           [0029]      FIG. 7  illustrates Klippel&#39;s loudspeaker protector, according to the prior art. 
           [0030]      FIG. 8  illustrates Klippel&#39;s another loudspeaker protector, according to the prior art. 
           [0031]      FIG. 9  illustrates Kohut&#39;s loudspeaker excursion limiter, according to the prior art. 
           [0032]      FIG. 10  illustrates Poletti&#39;s amplifier with distortion effects, according to the prior art. 
           [0033]      FIG. 11  illustrates Bjerre&#39;s amplifier with frequency dependent amplitude regulation, according to the prior art. 
           [0034]      FIG. 12(A-C)  illustrates examples of proportional adder/subtracter, according to the present invention. 
           [0035]      FIG. 13  illustrates the symbol of a triode or triode emulator. 
           [0036]      FIG. 14  (A) illustrates the symbol of bass low pass filter, according to the present invention. 
           [0037]      FIG. 14  (B-E) illustrates frequency responses of some example filters that are bass low pass filters, according to the present invention. 
           [0038]      FIG. 14  (F-H) illustrates the implementation of some example filters that are bass low pass filters, according to the present invention. 
           [0039]      FIG. 15  (A) illustrates the symbol of bass high pass filter, according to the present invention. 
           [0040]      FIG. 15  (B-E) illustrates frequency responses of some example filters that are bass high pass filters, according to the present invention. 
           [0041]      FIG. 15  (F-H) illustrates the implementation of some example filters that are bass high pass filters, according to the present invention. 
           [0042]      FIG. 16  (A) illustrates the symbol of type 1 expander, according to the present invention. 
           [0043]      FIG. 16  (B) illustrates the output-input relation ship of a type 1 expander, according to the present invention. 
           [0044]      FIG. 16  (C-D) illustrate examples of type 1 expander, according to the present invention. 
           [0045]      FIG. 17  (A) illustrates the symbol of type 1 compressor, according to the present invention. 
           [0046]      FIG. 17  (B) illustrates the output-input relation ship of a type 1 compressor, according to the present invention. 
           [0047]      FIG. 17  (C-D) illustrate examples of type 1 compressor, according to the present invention. 
           [0048]      FIG. 18  (A) illustrates the symbol of type 2 compressor, according to the present invention. 
           [0049]      FIG. 18  (B-C) illustrates the output-input relationship of type 1 compressors, according to the present invention. 
           [0050]      FIG. 18  (D-E) illustrate examples of type 2 compressor, according to the present invention. 
           [0051]      FIG. 19  (A) illustrates the symbol of type 2 expander, according to the present invention. 
           [0052]      FIG. 19  (B-C) illustrates the output-input relationship of a type 2 expander, according to the present invention. 
           [0053]      FIG. 19  (D-E) illustrate examples of type 3 expander, according to the present invention. 
           [0054]      FIG. 20  (A) illustrates the symbol of type 3 expander, according to the present invention. 
           [0055]      FIG. 20  (B) illustrates an example of type 3 expander, according to the present invention. 
           [0056]      FIG. 21  (A) illustrates the symbol of type 3 compressor, according to the present invention. 
           [0057]      FIG. 21  (B) illustrates an example of type 3 compressor, according to the present invention. 
           [0058]      FIG. 22  (A) illustrates the symbol of voltage driver, according to the present invention. 
           [0059]      FIG. 22  (B) illustrates an example of voltage driver, according to the present invention. 
           [0060]      FIG. 23  (A) illustrates the symbol of current driver, according to the present invention. 
           [0061]      FIG. 23  (B) illustrates an example of current driver, according to the present invention. 
           [0062]      FIG. 24  (A) illustrates the symbol of type 1 Rp/Power supply emulator, according to the present invention. 
           [0063]      FIG. 24  (B) illustrates an examples of type 1 Rp/Power supply emulator, according to the present invention. 
           [0064]      FIG. 25  (A) illustrates the symbol of type 2 Rp/Power supply emulator, according to the present invention. 
           [0065]      FIG. 25  (B-C) illustrate examples of type 2 Rp/Power supply emulator, according to the present invention. 
           [0066]      FIG. 26  illustrate block diagram of the invented tube amplifier emulator, according to the current invention. It was disclosed in my said AES paper. 
           [0067]      FIG. 27  illustrates an example implementation of the block diagram illustrated in  FIG. 26 , according to the present invention. 
           [0068]      FIG. 28  (A-B) illustrate the first preferred embodiment of said tube amplifier emulator, according to the present invention. 
           [0069]      FIG. 29  (A-B) illustrate the second preferred embodiment of said tube amplifier emulator, according to the present invention. 
           [0070]      FIG. 30  illustrates the third preferred embodiment of said tube amplifier emulator, according to the present invention. 
           [0071]      FIG. 31  (A)-B) illustrate the fourth preferred embodiment said tube amplifier emulator, according to the present invention. 
           [0072]      FIG. 32  illustrates fifth preferred embodiment said tube amplifier emulator, according to the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Analysis of the Triode Amplifier 
     Terms 
       [0073]    Throughout the specification and claims, the following terms take at least the meanings explicitly associated herein, unless the context clearly dictates otherwise. The meanings identified below are not intended to limit the terms, but merely provide illustrative examples for use of the terms. 
         [0074]    The term “coupled” can mean a direct connection between items, an indirect connection through one or more intermediaries, or communication between items in a manner that may not constitute a physical connection. 
         [0075]    The term “circuit” can mean a single component or a plurality of components, active and/or passive, discrete or integrated, that are coupled together to provide a desired function. 
         [0076]    The term “signal” can mean at least one current, voltage, charge, data, or other such identifiable quantity. A voltage signal can mean such identifiable quantity that represent a voltage and itself is not necessarily in the form of a voltage. A current signal can mean such identifiable quantity that represent a current and itself is not necessarily in the form of a current. 
         [0077]    Signal A is “proportional” to signal B may mean the AC part of signal A is substantially proportional to the AC part of signal B. The proportion coefficient may be positive or negative or zero. When signal A is proportional to signal B, signal B is also proportional to signal A. 
         [0078]    Signal A is “equivalent” to signal B may mean the AC part of signal A substantially equals to the AC part of signal B. 
         [0079]    A port is where signal is coupled to a circuit. A port can be an input port, an output port, or a port that is both input port and output port. Some times a port is just called a port, without mention its type. 
         [0080]    Signal A “contains” signal B means there signal A has information about signal B, and signal B can be recovered from signal A if needed, possibly by processing signal A with other signals. For example, if voltage signal A is a summation of voltage signal B and voltage signal C, then signal A contains signal B, because later on signal B can be recovered by subtracting signal C from signal A. For another example, signal A contains signal A itself. This term specify only the relationship between signals by value, it does not limit which signal drives the other. 
         [0081]    A “weighted summation” of two or more input signals is a signal that is a summation of each of the input signals, each with a proportion coefficient that can be positive or negative, respectively. 
       Proportional Adder/Subtracter 
       [0082]      FIG. 12  (A-C) illustrate some examples of proportional adder/subtracters. A proportional adder/subtracter has at least a first input port  1 , a second input port  2 , optionally other input ports, such as  3 , and an output port  4  where the signal at said output port  4  is a weighted summation of signals received from said first input port  1 , said second input port  2 , and said optionally other input ports, such as said port  3 . The weighting coefficients may individually be positive or negative. 
         [0083]    In  FIG. 12  (A), a resistor network is used to proportionally sum up voltages at the input ports, each with a corresponding coefficient. A first input port  1  is connected to an output port  4  through resistor  5 . A second input port  2  is connected to said output port  4  through resistor  6 . An input port  3  is connected to said output port  4  through resistor  7 . Said output port  4  is connected to ground through resistor  8 . The output voltage at said output port  4  is a weighted summation of the input voltages at said first input port  1 , said second input port  2  and said input port  3 . 
         [0084]    In  FIG. 12  (B), a first input port  1  is connected to an output port  4 . A second input port  2  is connected to said output port  4 . An input port  3  is connected to said output port  4 . The input currents at said first input port  1 , said second input port  2  and said input port  3  are added up and sent to said output port  4 . 
         [0085]    In  FIG. 12  (C), a first input port  1  is connected to the negative input port of an operational amplifier  9  through resistor  10 . A second input port  2  is connected to the positive input port of an operational amplifier  9  through resistor  11 . The negative input port of said operational amplifier  9  is connected to the output port of said operational amplifier  9  through resistor  12 . The positive input port of said operational amplifier  9  is connected to ground through resistor  13 . The voltage at an output port  4  is proportional to the weighted summation of the voltages at said first input port  1  and said second input port  2 , each with a proportion coefficient, respectively. The proportion coefficient for voltage at said first input port  1  is negative while the proportion coefficient for voltage at said second input port  2  is positive. 
       Triode or Triode Emulator 
       [0086]    Triodes have specific nonlinearities of their own, So triodes can he used for their nonlinearity. When triode is not available, or is not appreciated for any reasons, a triode emulator can be used instead. For example, a pentode can be wired to behave like a triode. For example, the screen and grid can be connected together so that the pentode will behavior like a triode. A transistor or FET can be wired such that the collector (transistor) or drain (FET) has feedbacks to the base (transistor) and grid (FET), so that a transistor or FET will behave like triode. 
       Bass Low Pass Filter 
       [0087]    Let me first define bass frequency range. Because speaker distortion is mostly produced by low frequency signals in the audio frequency range, we are interested in the low frequency range of the audio frequency range. We call such a low frequency range bass frequency range, which is typically, and is not limited to, 20 Hz to 200 Hz. For example, for one audio processing system, such a range might be from 50 Hz to 250 Hz. For another one, it might be from 15 Hz to 100 Hz. 
         [0088]      FIG. 14  (A) illustrates the symbol of a bass low pass filter  14 . Said bass low pass filter  14  has at least an input port  15  and an output port  16 . Said bass low pass filter  14  receives an input signal from the input port  15  and produces an output signal to the output port  16  such that in the majority part of said bass frequency range, for a fixed input amplitude, the higher the input frequency is, the lower the output amplitude is. 
         [0089]      FIG. 14  (B) illustrates the frequency response of an integrator. An integrator has frequency response  17  reversely related to the frequencies of the input signal, for any frequencies, including those in the bass frequency range  18 . Thus an integrator is a bass low pass filter. 
         [0090]      FIG. 14  (C) illustrates the frequency response  19  of a low pass filter. The cut off frequency  20  is not much higher than said bass frequency range  21 , thus the frequency response is reversely related to the frequencies of the input signal, and this low pass filter is a bass low pass filter. 
         [0091]      FIG. 14  (D) illustrates the frequency response  22  of a band pass filter. The upper cut off frequency  23  is not much higher than said bass frequency range  24 , and the lower cut off frequency  25  is low enough, thus in said low frequency range  24 , the frequency response is reversely related to the frequencies of the input signal, and this band pass filter is a bass low pass filter. 
         [0092]      FIG. 14  (E) illustrates the frequency response  26  of a band reject filter. The lower cut off frequency  27  is not much lower than said bass frequency range  28 , and the upper cut off frequency  29  is high enough, thus in said low frequency range  28 , the frequency response is reversely related to the frequencies of the input signal, and this band reject filter is a bass low pass filter. 
         [0093]      FIG. 14  (F) illustrates an example of the bass low pass filter. The input port  15  is coupled to one port of a resistor  30 . The other port of said resistor  30  is coupled to the negative input port of an operational amplifier  31 . Said negative input port of said operational amplifier  31  is coupled to one port of a capacitor  32 . The other port of said capacitor  32  is coupled to the output port of said operational amplifier  31 . The positive input port of said operational amplifier  31  is grounded. Said output port of said operational amplifier  31  is coupled to the output port  16 . This is an integrator circuit that has the frequency response reversely related to the frequencies of the input signal. Thus this circuit acts as bass low pass filter. 
         [0094]      FIG. 14  (G) illustrates another example of the bass low pass filter. The input port  15  is coupled to one port of a resistor  33 . The other port of said resistor  33  is coupled to the negative input port of an operational amplifier  34 . Said negative input port of said operational amplifier  34  is coupled to one port of a capacitor  35 . The other port of said capacitor  35  is coupled to the output port of said operational amplifier  34 . Said negative input port of said operational amplifier  34  is coupled to one port of a resistor  36 . The other port of said resistor  36  is coupled to the output port of said operational amplifier  34 . The positive input port of said operational amplifier  34  is grounded. Said output port of said operational amplifier  34  is coupled to the output port  16 . This is a low pass filter circuit. If the cut off frequency is chosen not to be much higher than said bass frequency range, This circuit acts as bass low pass filter. 
         [0095]      FIG. 14  (H) illustrates yet another example of the bass low pass filter. The input port  15  is coupled to one port of a resistor  37 . The other port of said resistor  37  is coupled to the first port of a capacitor  38 . The other port of said capacitor  39  is grounded. The first port of said capacitor  38  is coupled to the output port  16 . This is an integrator circuit thus acts as bass low pass filter. 
       Bass High Pass Filter 
       [0096]      FIG. 15  (A) illustrates a bass high pass filter  40 . Bass high pass filter  40  has at least an input port  41  and an output port  42 . A bass high pass filter  40  receives an input signal from the input port  41  and produces an output signal to the output port  42  such that in the majority part of said bass frequency range, for a fixed input amplitude, the higher the input frequency is, the higher the output amplitude is. 
         [0097]      FIG. 15  (B) illustrates the frequency response of a differentiator. A differentiator has frequency response  43  positively related to the frequencies of the input signal, for any frequencies, including those in the bass frequency range  44 . Thus a differentiator is a bass high pass filter. 
         [0098]      FIG. 15  (C) illustrates the frequency response  45  of a high pass filter. The cut off frequency  46  is not much lower than said bass frequency range  47 , thus the frequency response is positively related to the frequencies of the input signal, and this high pass filter is a bass high pass filter. 
         [0099]      FIG. 15  (D) illustrates the frequency response  48  of a band pass filter. The lower cut off frequency  49  is not much lower than said bass frequency range  50 , and the upper cut off frequency  51  is high enough, thus in said low frequency range  50 , the frequency response is positively related to the frequencies of the input signal, and this band pass filter is a bass high pass filter. 
         [0100]      FIG. 15  (E) illustrates the frequency response  52  of a band reject filter. The upper cut off frequency  53  is not much higher than said bass frequency range  54 , and the lower cut off frequency  55  is low enough, thus in said low frequency range  54 , the frequency response is positive related to the frequencies of the input signal, and this band reject filter is a bass high pass filter. 
         [0101]      FIG. 15  (F) illustrates an example of the bass high pass filter. The input port  41  is coupled to one port of a capacitor  56 . The other port of said capacitor  56  is coupled to the negative input port of an operational amplifier  57 . Said negative input port of said operational amplifier  57  is coupled to one port of a resistor  58 . The other port of said resistor  58  is coupled to the output port of said operational amplifier  57 . The positive input port of said operational amplifier  57  is grounded. Said output port of said operational amplifier  57  is coupled to the output port  42 . This is a differentiator circuit that has the frequency response positively related to the frequencies of the input signal. Thus this circuit acts as bass high pass filter. 
         [0102]      FIG. 15  G illustrates another example of the bass high pass filter. The input port  41  is coupled to one port of a capacitor  59 . The other port of said capacitor  59  is coupled to the negative input port of an operational amplifier  60 . Said input port  41  is also coupled to one port of a resistor  61 . The other port of said resistor  61  is coupled to said negative input port of said operational amplifier  60 . Said negative input port of said operational amplifier  60  is coupled to one port of a resistor  62 . The other port of said resistor  62  is coupled to the output port of said operational amplifier  60 . The positive input port of said operational amplifier  60  is grounded. Said output port of said operational amplifier  60  is coupled to the output port  42 . This is a high pass filter circuit. If the cut off frequency is chosen not to be much lower than said bass frequency range, This circuit acts as bass high pass filter. 
         [0103]      FIG. 15  (H) illustrates yet another example of the bass high pass filter. The input port  41  is coupled to one port of a capacitor  63 . The other port of said capacitor  63  is coupled to the first port of a resistor  64 . The other port of said resistor  65  is grounded. Said first port of said resistor  64  is coupled to the output port  42 . This is a differentiator circuit circuit so acts as bass high pass filter. 
       Type 1 Expander 
       [0104]      FIG. 16  (A) illustrates a type 1 expander  66 . Said type 1 expander  66  has at least one input port  67  and one output port  68 . The relationship between the output signal taken from said output port  68  and the input signal fed into said input port  67  is that, at least on one extreme of the operation range of said type 1 expander, when said input signal changes away from the operation point of said type 1 expander, the absolute value of the rate of change of said output signal monotonously increases. It is not required that it strictly increases.  FIG. 16  illustrates an example of the relationship between said output signal and said input signal, depicted as a function curve. Denote it the type 1 expander curve. In  FIG. 16  (B),  69  is near said extreme of the operation range, which shows that when said input signal decreases from the operation point  70 , the absolute value of the rate of change of said output signal monotonously increases (The slop of the function curve becomes steeper). It does not matter how the function curve looks like at the opposite extreme. It can look like, for example,  71 , 72 , 73 , or other shapes. It is not required that a substantial portion of the function curve near operation point is linear. The function curve is preferably smooth. It is noted that if said input signal or said output signal or both, of the function curve, are added with fixed values, are negated, or are manipulated with the combination of the two, the resulted function curves are still type 1 expander curves, and the type 1 expander is still a type 1 expander. 
         [0105]      FIG. 16  (C) illustrates an example circuit of said type 1 expander. The input current signal is fed into the input port  67  of said circuit. The output port  68  of said circuit produces output voltage signal. Said input port  67  is coupled to one port of a resistor  74 . The other port of said resistor  74  is coupled to the positive port of a diode  75 . The negative port of said diode  75  is grounded. Said input port  67  is also coupled to the output port  68 . When said input current signal is large, said diode  75  is almost fully conductive, so said output voltage signal is essentially said input current signal times the value of said resistor  74  plus voltage drop of said diode  75  (usually around 0.6V for silicon diodes). When said input current signal decreases, the rate of decreasing of said output voltage signal increases. Thus this circuit acts as a type 1 expander. 
         [0106]      FIG. 16  (D) illustrates another example circuit of said type 1 expander. The input signal is fed into the input port  67 . The output signal is taken from the output port  68 . The logarithm amplifier  76  is a logarithm circuit taken from FIG. 1 of National Semiconductor Application Note 311, “Theory and Application of Logarithmic Amplifiers”. It is referred as “AN-311” in this application. Said input port  67  is coupled to the input port  77  of said logarithm amplifier  76 . Said input port  67  is also coupled to one port of a resistor  78 . The other port of said resistor  78  is coupled to the negative input port of a first operational amplifier  79 . The output port  80  of said logarithm amplifier  76  is coupled to one port of a resistor  81 . The other port of said resistor  81  is coupled to the negative input port of a second operational amplifier  82 . The positive input port of said operational amplifier  79  is grounded. Said negative input port of said operational amplifier  79  is coupled to one port of a resistor  83 . The other port of resistor  83  is coupled to the output port of said operational amplifier  79 . Said output port of said operational amplifier  79  is coupled to a port of a resistor  84 . The other port of said resistor  84  is coupled to said negative input port of said second operational amplifier  82 . Said negative input port of said operational amplifier  82  is coupled to one port of a resistor  85 . The other port of said resistor  85  is coupled to the output port of said second operational amplifier  82 . The positive input port of said operational amplifier  82  is grounded. The output port of said second operational amplifier  82  is coupled to said output port  68 . 
         [0107]    Said logarithm amplifier  76  has the transfer function of negated logarithm with base  10 . The output signal of said logarithm amplifier  76  is scaled and negated and added to the scaled input signal fed into said input port  67 . Thus, when said input signal is small, the output signal of said circuit is mostly contributed by said logarithm amplifier  76 , so the absolute value of the rate of change of said output signal of said circuit is large. When said input signal is large, the output signal of said circuit is mostly contributed by said first operational amplifier  79 , so that the absolute value of the rate of change of said output signal of said circuit is moderate. Thus said circuit acts as a type 1 expander. 
       Type 1 Compressor 
       [0108]      FIG. 17  (A) illustrates a type 1 compressor  86 . Said type 1 compressor  86  has at least one input port  87  and one output port  88 . The relationship between the output signal taken from said output port  88  and the input signal fed into said input port  87  is that, at least on one extreme of the operation range of said type 1 compressor, when said input signal changes away from the operation point of said type 1 compressor, the absolute value of the rate of change of said output signal monotonously decreases. It is not required that it strictly decreases.  FIG. 17  (B) illustrates an example of the relationship between said output signal and said input signal, depicted as a function curve. Denote it type 1 compressor curve. In  FIG. 17  (B),  89  is near said extreme of the operation range, which shows that when said input signal decreases from the operation point  90 , the absolute value of the rate of change of said output signal monotonously decreases (the slop of the function curve becomes less steep). It does not matter how the function curve looks like at the opposite extreme. It can look like, for example,  91 , 92 , 93 , or other shapes. It is not required that a substantial portion of the function curve near operation point is linear. The function curve is preferably smooth. It is noted that if said input signal or said output signal or both, of the function curve, are added with fixed values, are negated, or are manipulated with the combination of the two, the resulted new function curves are still type 1 compressor curves, and the type 1 compressor is still a type 1 compressor. 
         [0109]      FIG. 17  (C) illustrates an example circuit of said type 1 compressor. The input voltage signal is fed into the input port  87  of the circuit. The output port  88  of said circuit produces output voltage signal. Said input port  87  is coupled to the positive port of a diode  94 . The negative port of said diode  94  is coupled to one port of a resistor  95 . The other port of said resistor  95  is grounded. Said negative port of said diode  94  is coupled to the output port  88 . When the input voltage signal is large, said diode  94  is almost fully conductive, so the output voltage signal is essentially the input voltage signal minus the voltage drop of said diode (usually 0.6V for silicon diodes). When the input voltage signal decreases, the absolute value of the rate of change of said output signal decreases. Thus this circuit acts as a type 1 compressor. 
         [0110]      FIG. 17  (D) illustrates another example circuit of said type 1 compressor. The input signal is fed into the input port  87 . The output signal is taken from the output port  88 . An exponential amplifier  96  is taken from  FIG. 2  of said document AN-311. Said input port  87  is coupled to one port of a resistor  97 . The other port of said resistor  97  is coupled to the negative input port of a second operational amplifier  98 . The negative input port of a first operational amplifier  99  is coupled to one port of a resistor  100 . The other port of said resistor  100  is coupled to the output port of said first operational amplifier  99 . The positive input port of said first operational amplifier  99  is grounded. Said output port of said first operational amplifier  99  is coupled to a port of a resistor  101 . The other port of said resistor  101  is coupled to said negative input port of said second operational amplifier  98 . Said negative input port of said second operational amplifier  98  is coupled to one port of a resistor  102 . The other port of said resistor  102  is coupled to the output port of said second operational amplifier  98 . The positive input port of said operational amplifier  98  is grounded. Said output port of said second operational amplifier  98  is coupled to the input port  103  of said exponential amplifier  96 . The output port  104  of said exponential amplifier  96  is coupled to said output port  88  of said example circuit. Said output port  88  is also coupled to one port of a resistor  105 . The other port of said resistor  105  is coupled to said negative input port of said first operational amplifier  99 . 
         [0111]    Said exponential amplifier  96  has the transfer function of negated exponential with base  10 . The output signal of said exponential amplifier  96  is scaled and added to the negated and scaled input signal taken from said input port  87 , and the result is fed into said exponential amplifier  96 . Thus this circuit acts like a reverse of the expander example shown in  FIG. 16 . The method of such reversing is described in my paper “Loop Reversal Rule in Block Diagram and Signal Flow Graph Manipulation”, IEEE Signal Processing Letters, Volume 19, Issue 10, 2012, 672-675. It is referred as “my SPL paper” in this application. Thus this circuit acts as a type 1 compressor. 
       Type 2 Compressor 
       [0112]      FIG. 18  (A) illustrates a type 2 compressor  106 . Type 2 compressor  106  has at least a first input port  107 , a second input port  108  and an output port  109 . It takes at least a first input signal fed to said first input port  107 , a second input signal fed to said second input port  108 , and produces at least an output signal to said output port  109 , according to the following specification. 
         [0113]      FIG. 18  (B) illustrates the said specification. When said first input signal is fixed, the relationship between said output signal and said second input signal follow said type 1 compressor curve (call it the “first curve” in this paragraph only). When said first input signal is changed slightly, the relationship between said output signal and said second input signal still follows a type 1 compressor curve, which is substantially similar to said first curve, and is substantially parallel to said first curve, whose position is shifted to the left or right direction of said first curve, and the change of position from said first curve is substantially proportional to the change of said first input signal. In  FIG. 18 , curves  110 ,  111 ,  112 ,  113 ,  114 , and  115  represent type 1 compressor curves corresponding to different first input signals. 
         [0114]      FIG. 18  (C) illustrates the output characteristic of a typical triode, the 300B triode. When Vg, Vp and Ip are corresponding to said first input signal, said second input signal, and said output signal, a triode is an example of type 2 compressor according to said specification. Note that for different Vg&#39;s, the Ip vs Vp curves are similar but not identical. 
         [0115]      FIG. 18  (D) illustrates an example of the type 2 compressor specified by said specification. It is related to  FIG. 18  (C). The first input signal  107  is coupled to port  116  of said triode or triode emulator  117 . The second input port  108  is coupled to port  118  of triode or triode emulator  117 . The output port  109  is coupled to port  119  of said triode or triode emulator  117 . The output port  119  of triode or triode emulator  117  is also coupled to one port of a resistor  120 . The other port of said resistor  120  is grounded. When the value of said resistor  120  is small, it does not affect the characteristic of the triode or triode emulator much but is still capable of extracting the Ip signal. 
         [0116]      FIG. 18  (E) illustrate another example of the type 2 compressor. The first input port  107  is coupled to the first input port  1  of a proportional adder/subtracter  121 . The second input port  108  is coupled to the second input port of said proportional adder/subtracter  121 . The output port  4  of said proportional adder/subtracter  121  is coupled to the input port  87  of a type 1 compressor  86 . The output port  88  of said compressor  86  is coupled to the output port  109 . 
       Type 2 Expander 
       [0117]      FIG. 19  (A) illustrates a type 2 expander  122 . Type 2 expander  122  has at least a first input port  123 , a second input port  124  and an output port  125 . It takes at least a first input signal fed to said first input port  123 , a second input signal fed to said second input port  124 , and produces at least an output signal to said output port  125 , according to the following specification. 
         [0118]      FIG. 19  (B) illustrates the specification. When said first signal is fixed, the relationship between output signal and said second input signal follow said type 1 expander curve (call it the “first curve” in this paragraph only). When said first input signal is changed slightly, the relationship between output signal and said second input signal still follow a type 1 expander curve, which is similar to the said first curve, and is substantially parallel to said first curve, whose position is changed to the up or down direction of said first curve, the change of position from said first curve is substantially proportional to the change of said first input signal. In  FIG. 19  (B), curves  126 ,  127 ,  128 ,  129 ,  130 , and  131  represent type 1 expander curves corresponding to different first input signal. 
         [0119]      FIG. 19  (C) illustrate the Ip, Vp and Vg curve of atypical triode, the 300B triode. When Vg, Ip and Vp are corresponding to said first input signal, said second input signal, and said output signal, said typical triode is an example of type 2 expander according to said specification of type 2 expander. Note that for different Vg&#39;s, the Vp vs Ip curve are similar but not identical. 
         [0120]      FIG. 19  (D) illustrate an example of the type 2 expander specified by said specification. It is related to  FIG. 19  (C). The first input port  123  is coupled the first port  116  of a triode or triode emulator  117 . The second input port  124  is coupled to the positive input port of an operational amplifier  132 . The output port of said operational amplifier  132  is coupled to the base of a NPN transistor  133 . The collector of said NPN transistor  133  is connected to a positive power supply. The emittor of said NPN transistor  133  is coupled to the second port  118  of a triode or triode emulator  117 . Said second port  118  of a triode or triode emulator  117  is coupled to said output port  125 . The third port  119  of said triode or triode emulator  117  is coupled to a port of resistor  134 . The third port  119  of said triode or triode emulator  117  is also coupled to the negative input port of said operational amplifier  132 . The other port of said resistor  134  is grounded. Said operational amplifier  132  and said NPN transistor  133  forces a current Ip into said second port  118  of said transistor means  117 , and the resulted Vp is a function of both Vi and Ip. 
         [0121]      FIG. 19  (E) illustrates another example of the type 2 expander. The first input port  123  is coupled to the first input port  1  of a proportional adder/subtracter  121 . The second input port  124  is coupled to the input port  67  of a type 1 expander  66 . The output port  68  of said type 1 expander  66  is coupled to the second input port of said proportional adder/subtracter  121 . The output port  4  of said proportional adder/subtracter  121  is coupled to the output port  125 . 
       Type 3 Expander 
       [0122]      FIG. 20  (A) illustrates a type 3 expander  135 . Type 3 compressor  135  has at least an input port  136  and an output port  137 . 
         [0123]      FIG. 20  (B) illustrates an example of type 3 expander. The input port  136  is coupled to the input port  15  of a bass low pass filter  14 . The output port  16  of said bass low pass filter  14  is coupled to the input port  67  of a type 1 expander  66 . The output port  68  of said type 1 expander  66  is coupled to the output port  137 . 
         [0124]    Type 3 expander  135  selectively expands higher frequency components in said low frequency range so that it can be used in the tube amplifier emulator to treat signals with different frequencies and amplitude differently. 
       Type 3 Compressor 
       [0125]      FIG. 21  (A) illustrates a type 3 compressor  138 . Type 3 compressor  138  has at least an input port  139  and an output port  140 . 
         [0126]      FIG. 21  (B) illustrates an example of type 3 compressor. The input port  139  is coupled to the input port  87  of a type 1 compressor  86 . The output port  88  of said type 1 compressor  86  is coupled to the input port  41  of a bass high pass filter  40 . The output port  42  of said bass high pass filter  40  is coupled to the output port  140 . 
         [0127]    Type 3 compressor  138  is a reverse of Type 3 expander  135 . 
       Voltage Driver 
       [0128]      FIG. 22  (A) illustrates the symbol of a voltage driver  141 . A voltage driver has at least an input port  142 , an output port  143 , a first terminal  144  and a second terminal  145 . Said voltage driver receives input signal from said input port  142 , amplifies or attenuates it, and output a voltage between said first terminal  144  and said second terminal  145  that is substantially proportional to said input signal received from said input port  142 . The voltage between said first terminal  144  and said second terminal  145  is capable of driving loudspeakers or earphones. A signal proportional to the output current between said first terminal  144  and second terminal  145  is sent to said output port  143 . 
         [0129]      FIG. 22  (B) illustrates an example of said voltage driver. It has an input port  142 , an output port  143 , a first terminal  144  and a second terminal  145 . The input port  142  is coupled to the input port of a voltage driving power amplifier  146 . The output port of said voltage driving power amplifier is coupled to said output terminal  144 . Said output terminal  145  is coupled to said output port  143 , and also coupled to one port of a resistor  147 . The other port of said resistor  147  is grounded. Thus the output current flows out of said first terminal  141  flows back into said second terminal  145 , and further flows through said resistor  147  so the current signal is converted into voltage signal and is sent to said output port  143 . 
       Current Driver 
       [0130]      FIG. 23  (A) illustrates the symbol of a current driver  148 . A current driver has at least an input port  149 , an output port  150 , a first terminal  151  and a second terminal  152 . Said current driver receives input signal from said input port  149 , amplifies or attenuates it, and output a current between said first terminal  151  and said second terminal  152  that is substantially proportional to said input signal received from said input port  149 . The current between said first terminal  151  and said second terminal  152  is capable of driving loudspeakers or earphones. A signal proportional to the output voltage between said first terminal  151  and second terminal  152  is sent to said output port  150 . 
         [0131]      FIG. 23  (B) illustrates an example of said current driver. It has an input port  149 , an output port  150 , a first terminal  151  and a second terminal  152 . The input port  149  is coupled to the input port of a current driving power amplifier  153 . The output port of said current driving power amplifier is coupled to said first output terminal  151 . Said first output terminal  151  is coupled to said output port  150 . Said second output terminal  152  is grounded. Thus the output voltage between said first terminal  151  and second terminal  152  is sent to said output port  150 . 
       Type 1 Rp/Power Supply Emulator 
       [0132]      FIG. 24  (A) illustrates the symbol of a type 1 Rp/Power supply emulator  154 . Rp represents the resistance of primary winding of the output transformer found in a vacuum tube amplifier. A typical power supply found in a vacuum tube amplifier has low pass filter characteristic. According to said my AES paper, the effect of Rp and the power supply can be emulated with the Rp/Power supply emulator. Said type 1 Rp/Power supply emulator  154  has at least one input port  155  and one output port  156 . The input signal received from said input port  155  is passed through a low pass filter and the result is sent out to said output port  156 . 
         [0133]      FIG. 24  (B) illustrates an example of said type 1 Rp/Power supply emulator  154 . The input port  155  is coupled to a first input port  1  of a proportional adder/subtracter  157 , and is also coupled to the input port of a low pass filter  158  that has a cut off frequency close to one found in a typical vacuum tube amplifier high voltage power supply line (so called “B+”). The low pass filter is preferably first order or second order filter. The output of said low pass filter  158  is coupled to the second input port  2  of said proportional adder/subtracter  157 . The output port  4  of said proportional adder/subtracter  157  is coupled to said output port  156 . 
       Type 2 Rp/Power Supply Emulator 
       [0134]    According to said my SPL paper, a loop in a block diagram or a circuit can be reversed and the input output relationship of the block diagram or circuit is not affected. Thus if the Type 1 Rp/Power Supply Emulator is in a loop, it can be reversed to allow the loop to be reversed. The reversing of Type 1 Rp/Power Supply Emulator results in Type 2 Rp/Power Supply Emulator. 
         [0135]      FIG. 25  (A) illustrates the symbol of type 2 Rp/Power supply emulator  159 . Type 2 Rp/Power supply emulator  159  has at least one input port  160  and one output port  161 . The input signal received from said input port  160  is passed through a circuit with high pass filter characteristic and the result is sent out to said output port  161 . 
         [0136]      FIG. 25  (B) illustrates an example of type 2 Rp/Power supply emulator  159 . The input port  160  is coupled to the first input port  1  of a proportional adder/subtracter  162 . The output port  4  of said proportional adder/subtracter  162  is coupled to the output port  161 , and is also coupled to the input port of a low pass filter  163 . The output of said low pass filter  163  is coupled to the second input port of said proportional adder/subtracter  162 . This method of reversing is described in detail in said my SPL paoer. 
         [0137]      FIG. 25  (C) illustrates another example of type 2 Rp/Power supply emulator  159 . The input port  160  is coupled to the first input port  1  of a proportional adder/subtracter  164 . 
         [0138]    The output port  165  of said proportional adder/subtracter  164  is coupled to the input port of a high pass filter  166 . The output port of said high pass filter  166  is coupled to the output port  161 , and is also coupled to the second input port  2  of said proportional adder/subtracter  164 . The high pass filter is preferably first order or second order filter with a cut off frequency close to one found in a typical vacuum tube amplifier high voltage power supply line (so called “B+”). 
         [0000]    Embodiments of the Tube amplifier Emulator 
         [0139]      FIG. 26  illustrates one configuration of the invented methods and apparatus of tube amplifier emulator that was disclosed in said my AES paper. 
         [0140]    The first preferred embodiment is illustrated in  FIG. 28(A-B) , which is a redraw of  FIG. 26 . According to  FIG. 28(A) , Said tube amplifier emulator configuration has at least one input port  167 , one first output terminal  168 , one second output terminal  169 , one type 2 compressor  170 , one type 1 Rp/power supply emulator  171 , one first proportional adder/subtracter  172 , one second proportional adder/subtracter  173 , one type 3 expander  174 , and one voltage driver  175 . The input signal  176  is coupled to said input port  167 , which is coupled to the first input port  107  of said type 2 compressor  170 . The output port  109  of said type 2 compressor  170  is coupled to the first input port  1  of said first proportional adder/subtracter  172 . The output port  4  of said first proportional adder/subtracter  172  is coupled to the input port  142  of said voltage driver  175 . The input port  136  of said type 3 expander  174  is coupled to the output port  4  of said first proportional adder/subtracter  172 . The output port  137  of said type 3 expander  174  is coupled to the second input port  2 ′ of said second proportional adder/subtracter  173 . The output port  143  of said voltage driver  175  is coupled to the first input port  1 ′ of said second proportional adder/subtracter  173 . The output port  4 ′ of said second proportional adder/subtracter  173  is coupled to both the input port  155  of said type 1 Rp/power supply emulator  171  and the input port  108  of said type 2 compressor  170 . The output port  156  of said type 1 Rp/power supply emulator  171  is coupled to the second input port  2  of said first proportional adder/subtracter  172 . Said output terminal  168  is coupled to the first output terminal  144  of said voltage driver  175 . Said output terminal  169  is coupled to the second terminal  145  of said voltage driver  175 . The output terminals  168  and  169  are coupled to a loudspeaker or loudspeakers. 
         [0141]    In  FIG. 28  (B) the optional type 1 Rp/power supply emulator is removed. According to  FIG. 28(B) , the Rp/power supply emulator and corresponding proportional adder/subtracter are removed, compared to  FIG. 28 . Said tube amplifier emulator configuration has at least one input port  167 , one first output terminal  168 , one second output terminal  169 , one type 2 compressor  177 , one proportional adder/subtracter  178 , one type 3 expander  179 , and one voltage driver  180 . The input signal  176  is coupled to said input port  167 , which is coupled to the first input port  107  of said type 2 compressor  177 . The output port  109  of said type 2 compressor  177  is coupled to the input port  142  of said voltage driver  180 . The input port  136  of said type 3 expander  179  is coupled to the output port  109  of said type 2 compressor  177 . The output port  137  of said type 3 expander  179  is coupled to the second input port  2 ′ of said proportional adder/subtracter  178 . The output port  143  of said voltage driver  180  is coupled to the first input port  1 ′ of said proportional adder/subtracter  178 . The output port  4 ′ of said proportional adder/subtracter  178  is coupled to the input port  108  of said type 2 compressor  177 . Said output terminal  168  is coupled to the first output terminal  144  of said voltage driver  180 . Said output terminal  169  is coupled to the second terminal  145  of said voltage driver  180 . The output terminals  168  and  169  are coupled to a loudspeaker or loudspeakers. 
         [0142]      FIG. 29  (A-B) illustrate another preferred embodiment of the present invention. In this configuration a loop is reversed, compared to  FIG. 28 . Said tube amplifier emulator configuration has at least one input port  167 , one first output terminal  168 , one second output terminal  169 , one type 2 expander  181 , one type 1 Rp/power supply emulator  182 , one first proportional adder/subtracter  183 , one second proportional adder/subtracter  184 , one type 3 compressor  185 , and one voltage driver  186 . The input signal  176  is coupled to said input port  167 , which is coupled to the first input port  123  of said type 2 expander  181 . The second input port  124  of said type 2 expander  181  is coupled to the output port  4  of said first proportional adder/subtracter  183 . The first input port  1  of said first proportional adder/subtracter  183  is coupled to the output port  140  of the type 3 compressor  185 . The output port  140  of said type 3 compressor  185  is coupled to the input port  142  of said voltage driver  186 . The input port  139  of said type 3 compressor  185  is coupled to the output port  4 ′ of said second proportional adder/subtracter  184 . The output port  143  of said voltage driver  186  is coupled to the first input port  1 ′ of said second proportional adder/subtracter  184 . The second input port  2 ′ of said second proportional adder/subtracter  184  is coupled to the output port  125  of said type 2 expander  181 . The input port  155  of said type 1 Rp/power supply emulator  182  is coupled to the output port  125  of said type 2 expander  181 . The output port  156  of said type 1 Rp/power supply emulator  182  is coupled to the second input port  2  of said first proportional adder/subtracter  183 . Said output terminal  168  is coupled to the first output terminal  144  of said voltage driver  186 . Said output terminal  169  is coupled to the second terminal  145  of said voltage driver  186 . The output terminals  168  and  169  are coupled to a loudspeaker or loudspeakers. 
         [0143]    In  FIG. 29  (B) the optional type 1 Rp/power supply emulator is removed. According to  FIG. 29(B) , the Rp/power supply emulator and corresponding proportional adder/subtracter are removed, compared to  FIG. 29(A) . Said tube amplifier emulator configuration has at least one input port  167 , one first output terminal  168 , one second output terminal  169 , one type 2 expander  187 , one proportional adder/subtracter  188 , one type 3 compressor  189 , and one voltage driver  190 . The input signal  176  is coupled to said input port  167 , which is coupled to the first input port  123  of said type 2 expander  187 . The second input port  124  of said type 2 expander  187  is coupled to the output port  140  of the type 3 compressor  189 . The output port  140  of said type 3 compressor  189  is coupled to the input port  142  of said voltage driver  190 . The input port  139  of said type 3 compressor  189  is coupled to the output port  4 ′ of said proportional adder/subtracter  188 . The output port  143  of said voltage driver  190  is coupled to the first input port  1 ′ of said proportional adder/subtracter  188 . The second input port  2 ′ of said proportional adder/subtracter  188  is coupled to the output port  125  of said type 2 expander  187 . Said output terminal  168  is coupled to the first output terminal  144  of said voltage driver  190 . Said output terminal  169  is coupled to the second terminal  145  of said voltage driver  190 . The output terminals  168  and  169  are coupled to a loudspeaker or loudspeakers. 
         [0144]      FIG. 30  illustrate another preferred embodiment of the present invention. According to  FIG. 30 , a loop is reversed, compared to  FIG. 28(A) . Said tube amplifier emulator configuration has at least one input port  167 , one first output terminal  168 , one second output terminal  169 , one type 2 compressor  191 , one type 2 Rp/power supply emulator  192 , one first proportional adder/subtracter  193 , one second proportional adder/subtracter  194 , one type 3 compressor  195 , and one voltage driver  196 . The input signal  176  is coupled to said input port  167 , which is coupled to the first input port  107  of said type 2 compressor  191 . The output port  109  of said type 2 compressor  191  is coupled to the first input port  1  of said first proportional adder/subtracter  193 . The second input port  2  of said first proportional adder/subtracter  193  is coupled to the output port  140  of the type 3 compressor  195 . The output port  140  of said type 3 compressor  195  is coupled to the input port  142  of said voltage driver  196 . The input port  139  of said type 3 compressor  195  is coupled to the output port  4 ′ of said second proportional adder/subtracter  194 . The output port  143  of said voltage driver  196  is coupled to the first input port  1 ′ of said second proportional adder/subtracter  194 . The output port  161  of said type 2 Rp/power supply emulator  192  is coupled both to the second input port  2 ′ of said second proportional adder/subtracter  194  and to the input port  108  of said type 2 compressor  191 . The input port  160  of said type 2 Rp/power supply emulator  192  is coupled to the output port  4  of said first proportional adder/subtracter  193 . Said output terminal  168  is coupled to the first output terminal  144  of said voltage driver  196 . Said output terminal  169  is coupled to the second terminal  145  of said voltage driver  196 . The output terminals  168  and  169  are coupled to a loudspeaker or loudspeakers. 
         [0145]      FIG. 31(A-B)  illustrate another preferred embodiment of the present invention. According to  FIG. 31  (A), a loop is reversed, compared to  FIG. 28(A) . Said tube amplifier emulator configuration has at least one input port  167 , one first output terminal  168 , one second output terminal  169 , one type 2 expander  197 , one type 1 Rp/power supply emulator  198 , one first proportional adder/subtracter  199 , one second proportional adder/subtracter  200 , one type 3 expander  201 , and one current driver  202 . The input signal  176  is coupled to said input port  167 , which is coupled to the first input port  123  of said type 2 expander  197 . The input port  124  of said type 2 expander  197  is coupled to the output port  4  of said first proportional adder/subtracter  199 . The input port  1  of said first proportional adder/subtracter  199  is coupled to the output port  150  of said current driver  202 . The input port  136  of said type 3 expander  201  is coupled to the output port  150  of said current driver  202 . The output port  137  of said type 3 expander  201  is coupled to the second input port  2 ′ of said second proportional adder/subtracter  200 . The input port  149  of said current driver  202  is coupled to the output port  4 ′ of said second proportional adder/subtracter  200 . The first input port  1 ′ of said second proportional adder/subtracter  200  is coupled to the output port  125  of said type 2 expander  197 . The input port  155  of said type 1 Rp/power supply emulator  198  is coupled to said output port  125  of said type 2 expander  197 . The output port  156  of said type 1 Rp/power supply emulator  198  is coupled to the second input port  2  of said first proportional adder/subtracter  199 . Said output terminal  168  is coupled to the first output terminal  151  of said current driver  202 . Said output terminal  169  is coupled to the second terminal  152  of said current driver  202 . The output terminals  168  and  169  are coupled to a loudspeaker or loudspeakers. 
         [0146]    In  FIG. 31(B) , the optional type 1 Rp/power supply emulator is removed. According to  FIG. 31  (B), the Rp/power supply emulator and corresponding proportional adder/subtracter are removed, compared to  FIG. 31(A) . Said tube amplifier emulator configuration has at least one input port  167 , one first output terminal  168 , one second output terminal  169 , one type 2 expander  203 , one proportional adder/subtracter  204 , one type 3 expander  205 , and one current driver  206 . The input signal  176  is coupled to said input port  167 , which is coupled to the first input port  123  of said type 2 expander  203 . The input port  124  of said type 2 expander  203  is coupled to the output port  150  of said current driver  206 . The input port  136  of said type 3 expander  205  is coupled to the output port  150  of said current driver  206 . The output port  137  of said type 3 expander  205  is coupled to the second input port  2 ′ of said second proportional adder/subtracter  204 . The input port  149  of said current driver  206  is coupled to the output port  4 ′ of said proportional adder/subtracter  204 . The first input port  1 ′ of said proportional adder/subtracter  204  is coupled to the output port  125  of said type 2 expander  203 . Said output terminal  168  is coupled to the first output terminal  151  of said current driver  206 . Said output terminal  169  is coupled to the second terminal  152  of said current driver  206 . The output terminals  168  and  169  are coupled to a loudspeaker or loudspeakers. 
         [0147]      FIG. 32  illustrate another preferred embodiment of the present invention. According to  FIG. 32 , a loop is reversed, compared to  FIG. 28(A) . Said tube amplifier emulator configuration has at least one input port  167 , one first output terminal  168 , one second output terminal  169 , one type 2 compressor  207 , one type 2 Rp/power supply emulator  208 , one first proportional adder/subtracter  209 , one second proportional adder/subtracter  210 , one type 3 expander  211 , and one current driver  212 . The input signal  176  is coupled to said input port  167 , which is coupled to the first input port  107  of said type 2 compressor  207 . The output port  109  of said type 2 compressor  207  is coupled to the first input port  1  of said first proportional adder/subtracter  209 . The second input port  2  of said first proportional adder/subtracter  209  is coupled to the output port  150  of said current driver  212 . The input port  136  of said type 3 expander  211  is coupled to the output port  150  of said current driver  212 . The output port  137  of said type 3 expander  211  is coupled to the second input port  2 ′ of said second proportional adder/subtracter  210 . The input port  149  of said current driver  212  is coupled to the output port  4 ′ of said second proportional adder/subtracter  210 . The first input port  1 ′ of said second proportional adder/subtracter  210  is coupled to the output port  161  of said type 2 Rp/power supply emulator  208 . The input port  108  of said type 2 compressor  207  is coupled to said output port  161  of said type 2 Rp/power supply emulator  208 . The input port  160  of said type 2 Rp/power supply emulator  208  is coupled to the output port  4  of said first proportional adder/subtracter  209 . Said output terminal  168  is coupled to the first output terminal  151  of said current driver  212 . Said output terminal  169  is coupled to the second terminal  152  of said current driver  212 . The output terminals  168  and  169  are coupled to a loudspeaker or loudspeakers.