What is an Amplifier
authored by Giovanni Arigo
What is an amplifier? Most people know that it works by increasing the amplitude of the signals fed into it. Actually, to put it another way, we could say that the amplifier makes a new signal at its output, an enlarged model of the smaller, weaker signal fed into it. This operation can be compared to trying to magnify a photograph. If the original is a high quality image and if the operator has a steady hand, the magnified image will be similar to the original one. But if we are using an imperfect image to start with, or if the paper is very rough, or the operator’s hand shakes, the resulting magnified image will certainly be different from the original. While the original and magnified image as seen from a certain distance might appear to be the same, looking more closely, we can see the disappearance of certain particulars and the appearance of new ones.
Let’s look at the optical analogy further, in a way that might relate more closely to audio amplification. Think of what happens when we take a photo of something – the light coming from the subject is focused on the film by means of the objective lens. Such a film will be developed and printed. If the subject was originally far away, we could magnify the image on paper in the printing phase in a manner similar to the example above. We realize that, with such an operation that we can not magnify the subject as much as we want, because, over a certain enlargement, the deficiency of the objective lens, and most of all the grain of film do not allow us to see further details. The too much magnified image looks to us rather different from the original subject, appearing “flat”, out of focus, unnatural, and lacking in minute detail. In a like manner, the active devices used in electronic amplifiers being non-linear devices, these transistors, vacuum tubes, mosfets, etc., are very far from perfect amplifiers, their output signal (current) never is exactly proportional to the input signal (voltage or current). An amplifier must be linear, its output signal “y” must be proportional to the input signal “x”, such that y = Ax where “A” is the amplification (gain) and has to be a constant.
An Outline of Negative Feedback
Feedback and especially negative feedback is a design methodology, used by most amplifier designers, which allows them to create very linear amplifiers using non-linear components such as tubes, transistors, etc. It is interesting to note that the use of negative feedback, used in electronic amplifiers from the beginning of the 20th century, is a very common mechanism in other areas. For instance, when we drive a car, if for any reason our car starts to leave the road, we, noting this situation, correct the driving error with an action in the opposite direction. Let’s suppose, in a hypothetical situation, we add a time delay so that the driver’s reflexes are very slow – in the order of a few seconds. Now, the driver corrects the deviations of the car with a big time delay: he will take the curves, for instance, correctly but after a few seconds the car will go off the road. Here, the negative feedback does not work any more.
Negative Feedback in Amplifiers
Let us see what happens in an electronic amplifier with negative feedback. An amplifier is shown in block form in fig 1. A portion of the output signal y , ß*y , is fed back and subtracted from the input signal, x . The difference between x and ß*y is e and is the signal actually applied to the input of the main amplifier block, A . Note, that ß must be equal or less than 1. The total amplification, Ar , is given by
Ar = A/(1+Aß)
Let’s suppose, for instance, that the block A amplifies 1000 times, and ß is 0.1 (where 10% of the output signal is applied to the subtraction process). The real amplification of the actual input signal X is
Ar = 1000/(1 + 1000*0.1) ~ 9.9
This value is how the circuit magnified the input signal. The numbers used in this example could be thought of as typical in a number of commercial preamplifiers. what usually happens is to design a circuit with an amplification higher than what we need, in this situation about 10. This has other benefits besides the stable predictable amount of amplification. Distortion is reduced by a factor of 100 and the bandwidth is increased by a similar amount. This allows us to design the amplifier without concern about its open loop (before feedback) linearity and slow speed as the negative feedback will repair the deficiencies. It is just necessary to take care to realize the circuit with a sufficiently high amount of before feedback amplification. Let’s suppose that in the previous example, we want 1V of output from a preamplifier output. For this output, y, the input signal, x, will be 1/9.9 ~ 0.101 V. Note, however, that the actual amplifier driving signal is not x but e which is the difference between x and ßy and is 0.001 V or 1 mV or one hundredth of the input signal, x. This output level of 1V is a fairly high value, enough to drive most power amplifiers to 50W output or more. Therefore it follows that the output voltage of this preamplifier circuit will normally be somewhat lower than the previously calculated 1 mV.
As many of us know, the musical signal is not a simple sinusoid but can be thought of as a series of a lot of sinusoids with differing amplitudes and frequencies. Each of these sinusoids takes part in the information included in the sound. They make, for instance, the difference between the violin and the cello sound, the virtual position of the instrument between the loudspeakers, the reverberation of the recording space, etc. Even the smallest harmonics take part in some aspect of the sound, excluding some of them could cause some important information in the sound to be lost. It is interesting to note what has happened with the “DCC” and “MINIDISC” players. Because of the limited recording space available on these mediums, considerable signal compression of the music must be used to get reasonable recording time – the number of bits is considerably less than on a CD. These signal compression algorithms eliminate parts of the input signal that have been psychologically determined to be masked by the louder parts of the music signal. Thus the number of bits to represent the signal can be reduced over the encoding used in CDs. In reality, those who have listened critically to the DCC and MINIDISC machines have pointed out that they can detect the loss of information, for instance, in the depth of sound images. All of this brings out the importance of even the smallest signals in conveying important information.
If we think that the newer 24 bit 96kHz technology is going to sonically better the CD system with its 96dB of dynamic range, it would be instructive to look at the implications of the 1 to 65,000 ratio between the minimum and maximum sound values of the CD system’s 96 dynamic range on the preamplifier circuit we have been studying. Inside the 1 mV actual signal which drives our amplifier there are therefore components that are 65,000 times lower which are important for the completeness of our sound message. This extremely low level of signal is 15 nanovolts (15 billionth of a volt!). Remembering that the 1V output signal level we had set for analysis is the maximum level and most of the music level will be much lower than this leading to minimum signal levels a few nanovolts or less. It is to be noted that the open loop gain of 1000 in the block “A” in fig. 1 is not excessive. In fact, open loop gains much higher are routinely found in integrated circuit operational amplifiers used in real world preamplifier circuits – ranging from perhaps 1000 (60dB) to as much as 100,000,000 (160 dB)! Thinking about such open loop gains and the minimum levels in a 24 bit system (ratio of some 1 to 17 million) lead to unimaginably small actual input signals to amplifier circuits.
The purpose of the foregoing analysis is to show how incredibly small the actual amplifier input signals are when using overall negative feedback loop topologies in amplifier circuits.
What problems can arise from this?
As just discussed, the input signals to amplifier blocks with high values of negative feedback are so small as to be comparable to the thermal noise inside the components (resistors, transistors, tubes, etc.) and to the voltage values from the thermal agitation of the electrons inside matter itself. It is important to note that our preamplifier circuit with negative feedback, which has an open loop gain of 1000, does not amplify the noise 1000 times. If it did, we would hear a noise higher than our musical signal. This is because the negative feedback reduces the noise like it reduces distortion. For each signal (noise, distortion, disturbances) generated inside the A block in fig. 1 but not present in the input signal, x , comes back from the output through the ß block to make an opposite signal in order to cancel it. Actually, in our example, it is reduced 100 times. At the output, then, such internal A block signals are amplified not 1000 but 9.9 times. This mechanism is like the car example above: if there is not time delay inside the amplifier the negative feedback works well. The problem is that such time delays do exist. Amplifier designers use negative feedback to reduce distortion and widen bandwidth for circuits that are usually non-linear and slow. In contrast with simpler circuits that might use little or no feedback, they are non-linear and slow because the circuits are complex utilizing many amplification stages.
The result of this situation is that the signal fed back through the ß block to be subtracted from the input signal, x, is not equal to the error signal that we want to cancel because of the time delay in A, it arrives late. Let us consider what the error signal would look like for an input signal that is a square wave. Refer to fig. 2. The input signal x (1) is amplified and comes out delayed at the output y (2), and delayed and reduced by the ß division at the input to the subtractor function. It is obvious that until there is some returned signal from the output at the subtractor, that the error signal, e, will be as big as the input signal itself and of the form shown in (3) in fig. 2. In practice, due to the limited bandwidth and other particular large signal characteristics of the open loop block, A , the output signal either changes with some exponential first order or a more complicated higher order shape or linearly slews during the delay time depicted in fig. 2.
Noise is not like a square wave in that it is a random process containing a wide range of non harmonically related frequency components. The internal noise signal, originating in the Block A is modified by means of the negative feedback and is added to the driving signal e and is uncorrelated or unrelated to the main music signal components. The negative feedback, therefore, is almost able to do its duty in reducing the noise at the output, but, due to the delay in the block A, the remaining noise components could have amplitudes even higher than the original ones. Such components are sparce and sporadic, and for this reason they do not appear in a traditional noise measurement. Further, as the noise is usually expressed as an average value, the value is smaller than in reality.
For the same reasons, they are almost not audible. However, as these components have random frequency and not negligible amplitudes, they could to be added to the musical signal included into e and, therefore possibly delete or block out some important information during the block A delay time.
If we use an input signal a sinusoidal wave with a low amount of harmonic content and observe the amplified signal with an oscilloscope or spectrum analyzer, we do not notice any misbehavior or anything wrong. When a “modified noise component” appears (due to the above described mechanism) it is so short, a few milliseconds or less, that it is almost impossible to observe it even though a small portion of the signal could be blocked out. If, in contrast, the input signal is a musical signal which contained no steady state harmonic components, that is, more like a random noise signal in this regard, the modified noise component could cause some momentary loss of the music information. Further, these same modified noise components can add some information not in the original musical signal. The same reasoning as the preceding can be applied to other kinds of disturbance to the circuit like power supply noises, noise from nearby circuits, etc.
It is evident that the smaller the driving signal to the amplifier (that is the higher the amount of overall negative feedback used) the greater the potential for the effects described above.
Another problem that arises from the application of negative feedback around an amplifier block with delay is that the delayed component from the output arriving back at the input causes an echo effect. Such superposition of signals is said to cause noticeable alterations of the sound stage aspect of sound reproduction.
Some Possible Solutions
Negative feedback can work correctly if the amplifier that is to have negative feedback applied is very fast, has little internal noise, and has high immunity to induced disturbances. These conditions can be largely satisfied with the more expensive amplifier designs. It does cost money in design effort and parts cost to obtain these results.
The simpler and more “natural” result is to not use negative feedback at all. With this approach, the amplifier block A is made intrinsically linear. If we make a comparison between the amplifier of our previous example and a no feedback amplifier with the same gain of 10 we can see that the no feedback amplifier is directly driven with the input signal x of 0.1 V, a 100 times higher signal than the previous feedback amplifier example. It follows that the no feedback example is less sensitive to the disturbances outlined in the previous section. We therefore propose the following objectives:
1. Do not use negative feedback, not only the global overall type discussed above, but also the local type applied to each active device. Although this later type is less harmful than the global type, it is still to be avoided.
2. Use the minimum number of amplification stages. If it is possible, use only one. The less components the less are the manipulations and alterations of the delicate musical signals.
3. The signal level inside the circuit never to be smaller than the input signal itself.
4. The resultant amplifier still has to have the electrical characteristics (bandwidth, distortion level, etc.) comparable to those designs using negative feedback.
The only devices used in no feedback designs that satisfy points 1, 2, and 3 are vacuum tubes and used only in low level circuits like phono preamps, etc., otherwise there will be too much distortion. Using transistors, if we do not use negative feedback, there will be unacceptable distortions, much higher than with tube circuits.
Fig. 3 shows an example circuit using JFET active devices. Its amplification AV is given by Av = gm R2 where R2 is the drain resistor value and fm is the transconductance of the JFET device. However, since gm is not constant with the JFET drain current, the gm parameter is the cause of the distortion in the circuit of Fig. 3. The JFET as well as bipolar transistors are not linear devices because their transconductances (the ratio of their output current change to input voltage or current change) are not constant but change with their output currents.
The solution is to skillfully use complementary non-linearities. Combining equal devices two by two it is possible to eliminate their respective non-linearities. An example of this is shown in fig. 4. As in the circuit of fig. 3, the input signal is applied directly to the sensitive input (gate-source) of the device as R1 is fully bypassed by the capacitor C and is not attenuated as with global feedback circuits. The amplification of this circuit is given by Av = (R2+R3)/R2 and as such, there are only constant parameters. This circuit does have a deficiency in regard to its output impedance and the ability to handle large signals. An improved circuit is presented in fig. 5.
This last circuit satisfies all 4 of the points above and can be compared in parameters of distortion, bandwidth, noise level, etc. to traditional negative feedback circuits even though it was thought that these levels of performance could only be attained with negative feedback amplifiers.