This differential amplifier was specially designed for use in my VK-1 audio oscillator and VK-2 distortion meter where the requirements of ultra-low distortion and ultra-low noise are equally challenging. These requirements are mutually contradictory because for minimizing thermal noise the values of signal route resistors should be reduced but that creates loading problems in an amplifier and raises its distortion.
     Output linearity of even the best integrated op amps begins to notably degrade when driving loads of less than 600 Ohm with several volts output. To correct the matter, an additional output buffering is needed that leads to circuit complication. Discrete operational amplifiers is a good alternative, as this allows to get better characteristics (distortion, noise, loading capability) by choosing high-grade components and setting their optimal working conditions. They usually copy the circuit topologies of their integrated counterparts although there is full freedom to implement non-traditional circuit solutions.
     In this design I avoid the use of any push-pull configurations and the amplifier single-ended output operates in pure class-A that brings the circuit simplicity and excludes the whole bucket of problems associated with crossover or switch-off distortion. Basic circuit diagram of the offered amplifier is shown in Fig.1.

Fig.1. Basic circuit of the differential amplifier.

     Its first stage is a typical differential transistor pair (Q1, Q2) fed from a current generator (Q3) and loaded by a current mirror (Q4, Q5). The stage open-loop gain depends on degeneration resistors R1, R2 in the emitters of Q1, Q2, their usually taken values are 33 or 120 Ohm that provides a twofold change in gain, this choice may be necessary for optimization of other circuit parameters.
     The second amplifying stage is a cascode on Q6, Q7 which is dynamically loaded by an emitter follower (Q8) fed from a current generator on Q9. This compact inverting amplifier configuration proves to be excellent first of all by featuring extremely low distortion, its high frequency performance is exemplary too.
     The first simulation circuit I would like to represent (Fig.2) allows to obtain the amplifier open-loop characteristics. Here the Multisim 10 software performs the circuit virtual testing in an interactive mode when the placed in chosen points measurement probes and virtual distortion analyzer monitor the circuit parameters (voltage, current, frequency, distortion) in time domain until stopping simulation.
     To provide the amplifier open-loop conditions, the negative AC feedback from its output to the base of Q2 is blocked by capacitor C5. The input signal from an AC voltage source V1 is adjusted to get the amplifier exact 2V RMS output which drives a 360-Ohm load (R12). It is the minimum resistance I test the circuit with.

Fig.2. Simulation of the differential amplifier without feedback at 20kHz.

     The simulation result shown by the distortion analyzer is 0,213%THD at 20kHz, the program has calculated this figure from the Fourier analysis data. To obtain these detailed data for all three most characteristic frequencies 100Hz, 1kHz, 20kHz, the Multisim function of Fourier analysis is used, the amplifier output all the time being maintained at a 2V RMS level. Fig.3 represents the results of conducted Fourier analysis of this output in a tabular form.

Fig.3. Fourier analysis of the differential amplifier without feedback.

     Most responsible for the amplifier linearity is of course the output stage, just its accepted configuration ensures the measured distortion to be practically the same low (about 0,2%) over the whole audio frequency range. There is no special choice of the stage's transistors, old good BC556 and BD139 perform very well in every respect. The increased DC current of 33mA through the output transistors is an inevitable price of running them in class A, but I’ve never worried about their thermal condition and never used any heatsinks.
     The next characteristic of the differential amplifier without feedback is its open-loop gain. In this case the program AC analysis is activated to measure at specified circuit points the AC voltage magnitude relative to the frequency sweeping input test signal of a constant magnitude. The chosen points are the first stage output (net 8) and the amplifier main output (net 16, see Fig.1), the analyzed frequency range - 1Hz-10MHz. The analysis is carried out twice, with the degeneration resistors' values of 33 and 120 Ohms, this is illustrated by doubled traces in Fig.4, the higher is for R1,R2=33-Ohm, the lower - for R1,R2=120-Ohm, the difference in gain between them being 6dB.

Fig.4. AC analysis of the differential amplifier without feedback.

     As can be seen, the open-loop gain remains practically constant not only in the audio range, but also at frequencies up to 100kHz, its distribution between the amplifier stages is the following: 160 (44dB) for the first stage and 500 (54dB) for the second, the total gain figure - 80000 (98dB).
     Expressions for obtaining the above parameters analytically are fairly straightforward:

     For the above transistors we therefore have re1= re2=26/0,574=45-Ohm, re6=26/1,29=20-Ohm. Most typical values of current gain β for transistors BC556A (Q6) and BD139 (Q8) are correspondingly β6=170 and β8=100 (from datasheets).
     Substitution of all the values into expressions (1,2) and subsequent mathematics finally yield:

     The calculated open-loop gain of the amplifier stages completely confirms the obtained simulation data. Earlier, years ago I came practically to the same results when making real measurements in my laboratory.
     Closed-loop analysis of the differential amplifier will be carried out twice - both its inverting and non-inverting configurations are interesting and some comparisons may be made. These amplifier circuits are depicted in Fig.5,7 and represent the modified circuit of Fig.2. The output parameters of interactive simulation are left the same - 2V RMS output voltage, 20kHz frequency, a 360-Ohm load. The closed-loop gain of both circuits is chosen unity, it means the negative 100% feedback is applied. This decision is taken to find out the lowest achievable level of closed-loop distortion and to explore the amplifier high-frequency behavior in the heaviest conditions. Of course a compensation capacitor C2 is necessary but its value was selected optimal in both cases to prevent worsening the amplifier linearity near 20kHz.
     AC analysis of both amplifier circuits reveals an absolutely flat characteristic of the closed-loop gain from 1Hz up to 10MHz, the input signal being 1V (see Fig.6,8). The amplifier second stage exhibits the determined above constant gain of 500 until 100kHz, after that its -6dB/octave reduction begins (blue traces in Fig.6,8) due to the action of local feedback via capacitor C2 which ensures the amplifier HF stability with the applied overall feedback. Fortunately, all that takes place well above the audio range and doesn’t influence the performance there.

Fig.5. Simulation of the inverting amplifier configuration at 20kHz.

Fig.6. AC analysis of the inverting differential amplifier.

Fig.7. Simulation of the non-inverting amplifier configuration at 20kHz.

Fig.8. AC analysis of the non-inverting differential amplifier.

     Most interesting part of the amplifier testing is measuring its closed-loop distortion. The Multisim 10 function of distortion analysis is just relevant here because the frequency sweeping input test signal produces the amplifier output of a strongly constant magnitude (5,6Vp-p or 2V RMS) and continuous measurement of the distortion second and third harmonics within a specified 20Hz-20kHz range is therefore quite correct. The program doesn’t analyze higher harmonics of distortion, but in this circuit their contribution isn’t essential and they don’t practically affect the amplifier THD. The distortion analysis results are represented in Fig.9.

Fig.9. Distortion analysis of the differential amplifier with feedback.

     Note that harmonics’ magnitudes are expressed relative to the amplifier 2V RMS output (the fundamental), not relative to a fixed 1V-p level as it’s done in all cases by the program. Common for the inverting and non-inverting amplifier configurations is the second harmonic of distortion prevailing over the third and being well below -140dB within the audio 20Hz-20kHz range, the third - below -150dB. But it is not still a limit. Replacement of the heavy 360-Ohm load by a more comfortable 510-Ohm causes at least a 6dB distortion drop in both circuits for both harmonics.
     The main factor making the distortion such vanishingly small is the depth and effectiveness of the applied overall feedback. In this circuit the open-loop distortion of about 0,2% within 20Hz-20kHz is reduced proportionally to the feedback factor being for the unity closed-loop gain practically the same as the open-loop gain and constant in the audio range too (100dB). The theoretically expected closed-loop distortion minimum is therefore 0,2/100000=0,000002% or -154dB, so the experimentally obtained distortion figures aren’t far from that.
     A simple experiment can demonstrate this feedback action mechanism - it’s enough to increase the emitter degeneration resistances to 120-Ohm and the amplifier will respond to that by a 6dB distortion rise in exact proportion to the twofold reduction of the open-loop gain (see Fig.4). The tiny distortion figures may seem doubtful and not valid, therefore I was forced to check the data by simulating the amplifier circuit in another program - Microcap 9.
     This program conducts the Fourier analysis of the non-inverting amplifier configuration at a 1kHz frequency (Fig.10). The measured by Microcap 9 distortion is: 0,0000017% or -156dB (second harmonic) and 0,0000011% or -159dB (third harmonic). In Multisim 10 the figures are correspondingly -154dB and -163dB (see Fig.9). Conclusion from this test is obvious - both programs are right, yielding the pretty similar measurement data.

Fig.10. Simulation of the non-inverting amplifier configuration at 1kHz in Microcap 9.

     The best noise performance of the amplifier is achieved when using its non-inverting configuration, just this circuit is chosen for the Multisim noise analysis. Low-noise input transistors and minimum resistances in their emitters bring the amplifier output unweighted noise level down to -133dB relative to a 1V output within 20Hz-20kHz (see Fig.11). Naturally, this figure will degrade if introducing more than unity closed-loop gain. Circuitry around the amplifier can be low-impedance for noise minimization, the amplifier will drive it without compromising the high linearity.

Fig.11. Noise analysis of the non-inverting differential amplifier.

     The final procedure of the amplifier testing is obtaining its transient characteristic. Here its inverting configuration is fed from the generator producing at first a square-wave 20kHz and then 500kHz signals with a 4V amplitude and 0,1nsec rise/fall time. It’s clearly seen that the 500kHz output features a slew-rate of more than 30V/µsec.

Fig.12. Square-wave test of the inverting differential amplifier.

     The demonstrated above computer simulation is a powerful assistant in electronics designing for those who have mastered it. But this amplifier and other my items were being designed, built and tested when I didn't have even a computer and the main instruments in my hands were a pencil and a soldering iron. I dealt with sub-microvolt distortion and noise in reality, just at my table, and most of all feared any incorrectness in measurements. This work required a lot of time and efforts, in contrast with the present simulation which can be performed in minutes.
     Recently, I've developed the unprecedented in its reliability and accuracy method of measuring distortion with the help of my virtual VK-2 distortion meter which can perform the fully transparent interactive distortion measurements of fantastic sensitivity - below -170dB (0.0000003%) within 20Hz-20kHz, the automatic process of -175dB suppression of the fundamental frequency taking less than 3sec.
     On the virtual oscilloscope screen you can see the extracted "live" distortion harmonics of an amplifier or oscillator whose circuit is entered to the simulation program which contains already the VK-2 distortion meter circuit. Amplified by +80dB the exact RMS sum of these harmonics is measured confidently because it is free of any swamping noise and any added distortion being unavoidable in real distortion or spectrum analysis. The Multisim oscillator and the VK-2 virtual meter don't create distortion and noise by definition, this trick allows to investigate the linearity just of the device under test with the help of the classic, most right method - by removing the fundamental frequency from the analyzed signal. The accuracy of measuring the residual distortion harmonics can be easily verified by applying their calibrated amounts, say -120dB, to the meter's input and analyzing its output, this accuracy being better than 0.5dB at all audio frequencies.

Fig.13. VK-2 distortion measurement of the discrete differential amplifier at 16kHz.

     The test scheme of Fig.13 contains the discrete differential amplifier in its unity-gain inverting configuration, it is fed from the Multisim 10 non-distorting generator and its 2V-16kHz output drives a 380ohm load. This voltage is then normalized at 1V level and applied to the input of the active rejection filter block consisting of an input twin-T notch network, a high-performance discrete amplifier (K=100), a 100kHz low-pass filter and at last the system of fine automatic tuning of the rejection filter, its Q-factor is chosen Q=2 and it carries out more than -170dB suppression of the fundamental frequency within 20Hz-20kHz. The following then output amplifier (K=100) brings the total gain of the residuals to +80dB for measuring them by an ordinary RMS voltmeter, observing on the virtual oscilloscope screen and using them in the filter tuning. The whole process of measuring distortion takes 1.74sec, its result appears at the VK-2 meter output, and the measured distortion is shown on the screen and registered by an AC millivoltmeter, its RMS value being in this case 220μV/10000=22nV or -153dB relative to the 1V input. As can be seen, this distortion is mainly the second harmonic.

Fig.14. VK-2 distortion measurement of the discrete differential amplifier at 1kHz.

     The similar procedure was conducted and for a 1kHz test frequency, the obtained in 1.97sec RMS value of extracted distortion is 180μV/10000=18nV or -155dB relative to the 1V input, it appears to be the third 3kHz harmonic (see Fig.14). The described measurement method is transparent and very accurate, the above distortion figures are absolutely reliable and they are close to the results of Fourier analysis performed earlier (see Fig.9,10).
     The fact of practical creation of my VK-1 oscillator and VK-2 distortion meter and their really measured characteristics best of all confirm the claimed linearity of this differential amplifier which was the main building block of these instruments. And I am happy that the real and virtual measurement data match each other.
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