New high gain circuit.
The advantages of resistancecapacitance circuits for phasesplitting in pushpull amplifiers are now well recognized, a wide variety of circuits for this purpose having been evolved in the last decade or so. If these circuits are investigated it is found that they possess varying degrees of merit in producing symmetrical output voltages, but share the common disadvantage of inherently low gain. In fact, low gain would appear to be almost inherent in any phasesplitting arrangement. The circuit to be described in this article, however, will be shown to possess a very high degree of symmetry with, at the same time, a large amplification from only two valves. An overall amplification of more than 1,000 times can very easily be achieved with standard lowg_{m} valves.
Fig. 1. The basic cathodefollower type of phasesplitter.
In order to facilitate analysis and to effect a just comparison with other types, the circuit will be compared with, and developed from, a normal cathodefollower phasesplitter preceded by a pentode AF stage.
For the purposes of this article the amplification of a phasesplitting system will be regarded as the ratio of either output voltage (assuming the two to be sensibly equal) to the signal input voltage (i.e., amplification = ^{e}_{01}/^{e}_{s} or ^{e}_{02}/^{e}_{s} in Fig. 2).
Fig. 2. The combination of a phasesplitter with a preceding AF stage is shown here.
In other words, the gain of the system as a whole is twice that given. The cathode follower, Fig. 1, is perhaps the most generally used circuit because of its simplicity and the high degree of balance obtainable between ^{e}_{01} and ^{e}_{02}, at normal frequencies, being dependent, only on the accuracy of R_{L}; and R_{C}. It possesses, of course, the inherent disadvantage of a cathode follower in that its gain is slightly less than unity (Appendix Equation (2)).
If we now consider such an arrangement to be preceded by a pentode stage the circuit becomes that of Fig. 2 and the overall gain is nearly that of the pentode alone, about 100 times.
Let us now consider the factors which limit the gain of the circuit of Fig. 2. It is wellknown that the input impedance of a cathodefollower is extremely high, approximately 10 × (impedance between grid and cathode); consequently if the gridcathode impedance is made 250 kΩ the impedance to the right of 'LM' in Fig. 2 is 2.5 MΩ. In other words, the input circuit of V_{2} does not appreciably shunt R_{1} and the gain obtainable from V_{1} is determined almost entirely by R_{1}. The value of this resistance cannot, however, be increased indefinitely, owing to the fall in steady anode voltage of V_{1} and a practical maximum is about 250 kΩ 500 kΩ. Since the AC resistance of the pentode is very high (say 2.5 M&Omega) it follows that only a small fraction of the amplification factor can be realized as gain (since gain = μR_{1}/(R_{a1} + R_{1}). This is unfortunate, because the amplification factor is extremely high, about 4,500 being quite a normal value for a pentode.
Suppose, however, it were possible to use the very high input impedance of a cathodefollower as the actual load on V_{1}. Then, since this impedance is comparable with the AC resistance of the pentode, the amplification obtained would be greatly increased.
Fig. 3. A modified phasesplitter in which the coupling resistor R_{1} becomes part of the gridcathode impedance of the cathodefollower.
If the circuit to the right of LM in Fig. 2 is rearranged as shown in Fig. 3, the parallel impedance of R_{1} and R_{3} replaces the gridcathode impedance R_{gc} while the effective cathode load is still R_{c}. Consequently the AC conditions have not been changed by the rearrangement and the input impedance is still approximately 10 × R_{gc} (where R_{gc} = R_{1}R_{3}/(R_{1} + R_{3}). It is assumed that the reactances of C_{1} and C_{2} are negligible at the lowest working frequency.
We cannot, as the circuit stands at present, connect the point L directly to the anode of V_{1} since there is no means of supplying anode current to V_{1}. It will be seen, however, that N is at earth potential and there is no reason why we should not return this end of the resistor to + HT, which is also at earth potential, so far as AC is concerned. In this way we can provide a DC path to the anode of V_{1} without disturbing the AC conditions on V_{2}, while V_{1} still sees the input impedance of V_{1}, acting as a cathode follower, as its dynamic load.
Fig. 4. The practical form of the highgain phasesplitter and preceding stage.
The final phasesplitting circuit becomes that of Fig. 4, in which the component values are those used in the experimental model.
Using an EF36 strapped as a triode for V_{2}, R_{a2} = 10 kΩ and μ = 28; with the component values of Fig. 4 Equation (1) gives the input impedance R_{in} as 2.05 MΩ. It will be noted that R_{1}R_{3}/(R_{1} + R_{3}) = 168 kΩ.
Then the amplification of V_{1} is given by μ_{1}R_{in}/(R_{a1} + R_{1} = 2030) where μ_{1} = 4,500 and R_{a1} = 2.5 MΩ.
The gain of V_{2} as given by Equation (2) is 0.9; therefore the overall gain of the system ^{e}_{02}/^{e}_{s} = 2030 × 0.9 = 1860. It is of interest to note that Equation (3) in the Appendix, which was derived directly from the equivalent circuit of Fig. 6(b), gives the same value as that obtained by the foregoing physical argument.
Fig. 6. The equivalent circuit of Fig. 4 can be drawn in the forms shown at (a) and (b).
The degree of asymmetry between ^{e}_{01} and ^{e}_{02} must be regarded as of even greater importance than mere gain. Inserting numerical values in Expression (4) of the Appendix we obtain ^{e}_{01}/^{e}_{02} = 0.989.
The inherent unbalance is less than 1.2% and therefore completely negligible. It may be wondered why any asymmetry should exist in the system; however, a consideration of the equivalent circuit of Fig. 6(b), shows that the sum of the alternating anode currents flows in the cathode load whereas the anode current of V_{2} alone flows in the anode load. The ratio of the alternating components of the anode currents of V_{2} and V_{1} is, however, very large.
Design Considerations
The circuit was specifically developed to drive valves of the PX25 class, and the values are therefore chosen to give a large peak output rather than maximum gain. If it is required to drive valves requiring a smaller grid swing no doubt much higher values of gain can be achieved. It should be pointed out to those evolving their own designs that the dynamic load on V_{1} is very much greater than the DC load, while the AC load on V_{2} is less than the DC load.
For smaller output voltages, say up to 25 V RMS at each output point, the component values are not critical while other types of valve have been substituted with only minor circuit changes; e.g., bias and screen resistors. It is of interest to note that the EF36 strapped as a triode gave better results from a linearity point of view than any of the triodes investigated.
As with most cathodefollower systems, it is advisable to reduce the heatercathode voltage of V_{2} by using a separate heater supply for the stage, connected to an appropriately decoupled point on the HT supply.
In order to avoid loss of gain it is desirable to bypass the cathode bias resistors of each stage.
Table 1 gives the results obtained with the circuit of Fig. 4.
Table 1
It will be noted than the measured gain is somewhat less than the calculated value, the discrepancy is not however more than can be accounted for by variations in the actual values of components from those assumed.
Application of Circuit
The circuit has been used over a number of years in a wide variety of amplifiers and has proved to be remarkably stable and free from undesirable traits.
Fig. 5. The circuit of a complete amplifier including the output stage. Overall negative feedback is used.
A complete design is given in Fig. 5. KT66 valves strapped as triodes have been used in the output stage, this method of connection giving a performance roughly equivalent to that of the PX25 type with the added advantages of shorter grid swing, indirectlyheated cathodes and octal base.
Without negative feedback an output of 14.5 W is obtained with less than 0.025 V (RMS) input. If negative feedback is applied as shown in Fig. 5 the required input voltage for maximum output is raised to 0.25V (RMS). The negative feedback reduces the distortion content to 0.5% at maximum output, while the output impedance becomes 120/n^{2} Ω. It is illuminating to note that this latter value is less than that obtained by operating the same valves as a cathode follower stage. Using a good quality output transformer the response, with overall negative feedback, was measured to be within ± 1 db from 25  20,000 Hz. If an output transformer of poorer quality is used the degree of feedback may have to be slightly reduced in order to satisfy the Nyquist stability criterion.
Where a greater output is required the KT66 valves can be operated as tetrodes in the normal manner and 35 W can then be obtained. The author favours however the use of four valves operating as triodes in parallel pushpull where a large output is desired.
No originality is claimed for the circuit, as a search of the literature has shown that it appeared in the USA some years ago; however, so far as the author is aware no analysis of the circuit has previously been published.
Appendix
