6L6 VACUUM TUBE AMPLIFIER


Vacuum Tube Amplifier with 4 6L6s in Parallel Push-Pull






Preliminary Remarks:-

The amplifier is based on the design philosophy and architecture used in the 6V6 amplifier.
A simplified diagram is shown below:-

(1) Plate Current Feedback

  The total plate current on either side of the push-pull class A amplifier is sensed in a 27 ohm resistor. This provides about 20 db of feedback over the 6L6 output tubes.
Extra feedback is produced by the 120 ohm unbypassed cathode resistors.
The result is:-
[1] The distortion in the output stage is reduced by a fator greater than 10.
[2] The output impedance is high - virtually infinite for all practical purposes.
[3] The low frequency and high frequency response of this inner loop is tailored to achieve a transfer function which aids stability in the overall feedback loop.
The low frequency turnover is about 0.5Hz and the high frequency turnover about 500KHz. This takes it outside the active frequency range of the main loop.

(2) Input Stage - Stabilising Networks

  The input stage consists of two frame grid triodes (V1a,V1b) connected in cascode.
This gives a low input capacity and a high output resistance.
A two terminal R-C network across the 60k load of the cascode tailors the open loop high frequency response to allow a high degree of feedback with stability.
The cathode follower (V3b) gives a low output impedance to drive an R-C network which tailors the low frequency response for stability in the main feedback loop.

(3) Phase Splitter

 The phase splitter consists of a unity gain operational amplifier.
Because of the high forward gain ( >> 200 ) the phase splitter has a high bandwidth and very low drift over time.
The operational amplifier is the cascode ( V2a, V2b ) and the cathode follower ( V3b ).

(4) Output Feedback Network

 A feedback network around the output transformer splits the feedback into a low and high frequency path.
The current drive to the primary of the output transformer results in the following transfer functions:-
[1] At high frequencies:-
 (a)The stray capacity across the primary produces a pole which gives an ultimate slope of 6db/octave and a phase change of -90 degrees.
 (b)The primary - secondary leakage inductance produces another pole with the same result.
[2] At low frequencies:-
  The primary inductance and reflected resistive load produce a pole which gives an ultimate slope of 6db/octave and a phase change of +90 degrees.
  The extra pole appearing on the transformer secondary output at high frequencies limits the overall feedback.
One of the most fundamental rules in the use of feedback is the following:-

Feedback must come from the output, not from some variable related to it.

  The network is designed to take feedback from the secondary (output) over the audio band up to 37.4KHz. and, above that, from the primary.
If the transformer is ideal, the network has a flat response.

(5) Tube Complement

The 6V6 amplifier used tubes current in 1938. Many of these are now in short supply.
The tubes in the 6L6 amplifier are all in current production, althouigh the 6L6 and the ECC82/12AU7 could hardly be called "modern".
The 6L6 was designed by Otto Schade of RCA in 1936, although its genesis was not in the USA, but in the UK.

  Beam Power Tubes by Otto Schade IRE Feb. 1938 pp 320-364

 Philips suppressed the secondary emission from the plate of a tetrode by a potential minimum produced by a suppressor grid at cathode potential.
J.Owen Harries in the UK realised that a potential minimum would be produced by space charge if the screen - plate distance was increased.
Cabot Bull and Sidney Rodda of EMI made further improvements including the introduction of beam forming plates.
Production difficulties initially prevented the tube from going into production in the UK.

  Puzzle : The detail design of this amplifier shows that the distortion and response depend entirely on the circuit design NOT the vacuum tube.
Yet advertising describes some 6L6 tubes as having "smooth"lows.
This seems to be against all the laws of Physics, but may herald the start of a new religion.
The transit time of an electron in a 6L6 is of the order of a nanosecond: far too fast to have any effect at audio frequencies.
There is a subtle effect at slow speeds: far too slow to have any effect at audio frequencies:-
A voltage step applied to the grid of a tube produces a step in plate current. This drops back by about 3% in tenths of a second.
Electrolysis occurs in the cathode, the emission drops, the potential minimum near the cathode retreats towards the cathode and the plate current decreases.
Tube pulse amplifiers have slow speed networks to equalise the effect.

  The ECC82 low mu double triode has been a workhorse since the late forties.
The ECC88 is a high slope medium mu frame grid tube.
The very small grid cathode spacing in frame grid tubes causes breakdown problems - especially during warm up.
In the absence of cathode emission, an estimate of the electric field strength, E, at the cathode is given by:-
E = Vgk/dgk
The stretched grid wire has a very small diameter, and so the grid surface has a small radius of curvature - greatly increasing the field strength E.
Large grid cathode voltages probably start field emission at the surface of the grid. The discharge then goes on to destroy the cathode.
Very large voltages can occur between grid and cathode during warm up before full cathode emission is reached.
Small neon tubes across critical points limit the voltage to the striking voltage of the neon.
The added parallel capacity is very small ( 0.3 to 0.4 pf ) and has negligible effect with the neon dormant.
The input is also protected, since it may be driven from a vacuum tube preamplifier.


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Full Circuit Diagram:-

 Note:
The five circuit blocks can be printed out and joined.


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Detailed Discussion:-

[A] 6L6 Output Stage

(1) Simplified Circuit Diagram

6L6 VACUUM TUBE AMPLIFIER


Simplified Output Stage



(2) 6L6 Screen Resistor

   The only convenient point to sense current is the cathode of the 6L6.
The 6L6 cathode current is the sum of the plate and screen current.
The plate - screen characteristics of the 6L6 are shown opposite and indicate that:-
[1] The ratio of screen to plate current is constant for high plate voltages.
[2] As the plate voltage drops below the screen voltage, the screen current kicks up in a highly non-linear manner, so the unmodified cathode current can no longer be used for feedback.
The plate current is the signal of interest.
At signal frequencies the screen current must be subtracted from the cathode current to get the plate current.
The screen current is shunted through a capacitor which has a much lower impedance over the audio band than the screen dropping resistor.
The inclusion of a screen dropping resistor modifies the behaviour of the output stage when operating at full power output and during overload conditions.
At very high prolonged power outputs the average screen current increases and the DC screen voltage drops reducing the power output, and protecting the 6L6 from excessive screen dissipation and failure.
For a normal audio signal the peaks have a small duty ratio and there is no limiting of peak power.
Amplifiers with the screens connected directly to high tension are prone to failure under prolonged overloads.

  The 22uF screen bypass capacitors are returned directly to the cathodes, so the current flowing through the cathode bias resistor is the plate current. This is true over the working frequency range of the amplifier.

  In the 6V6 amplifier, the screen capacitor current was sensed by a shunt and subtracted from the total cathode current in a low level stage.

(3) Stabilisation of Tube Operating Points

 Each 6L6 has its own screen, grid and cathode circuit.
Trouble with any tube is isolated and easily diagnosed.
The individual screen and cathode resistors provide DC stabilisation of the tube operating point.
The current in each 6L6 must be summed in order to provide a feedback reference. This implies a common resistor and a compromise in the isolation beween the two output tubes. The common resistor must be large enough to generate the required amplitude for feedback, but small enough to allow relatively independent operation of each tube.
The common resistor is 27 ohms and a further cathode resistor of 120 ohms is added for each tube.
The removal or failure of one tube then does not produce excessive dissipation in the other tube.
The total cathode current from all four 6L6s goes to ground through a common 1 ohm resistor.
If the push pull stage is balanced, no signal will be developed across this resistor. This can be used for the initial set-up. The internal feedback loops maintain freedom from drift over long periods.
The voltage produced by the plate current across the 27 ohm resistor is fed back directly into the cathode of the input ECC82 triode V1.
The 4.49 volt DC voltage acts as bias on V1. This is not desirable, since it is generated by the output tubes. Any bias should be generated by the plate current of V1 to give degeneration and stabilisation of the tube operating point.
AC coupling through a large capacitor would remove this effect, but make the low frequency feedback stabilisation of the current loop more difficult.
Another solution is to choose an operating point for V1 which requires a bias much greater than 4.49V, so the bulk of the bias can be produced with a cathode bias resistor.
The choice of a low mu triode, together with a low plate current of 0.5 Ma, requires a bias of 10.5 volts - allowing 6 volts of self bias and significant DC degeneration.
The distortion in both triode stages is small comparegd with distortion in the output stage. No local feedback is required in these stages, so both cathode resistors are bypassed to give maximum gain in the current loop.


(4) Low Frequency Response of Current Loop

    The low frequency response of the current feedback loop is shown opposite.
The turnover frequency is lower than 1Hz. This is below the active frequency range of the main overall loop, and so does not limit the degree of feedback in this loop.
In order to stabilise the low frequency response of the current loop, one of the poles lying on the real axis in the forward path must have a much smaller time constant ( higher frequency ) than the others.
This pole is produced by the coupling capacitors and grid leak resistors of the 6L6 output stage and gives a turnover frequency of about 10Hz.
It is important to keep this frequency as high as possible for the following reasons:-
  (1) During overload the 6L6 grid current rapidly charges the coupling capacitor and the resulting change in bias can paralyse the amplifier. Paralysis time decreases with the coupling time constant.
  (2) The 6L6 grid coupling capacitor should be a high quality 630 volt capacitor, so smaller values of capacitance reduce the physical size.
  (3) Grid current flowing through the grid leak resistor produces a spurious grid bias. The grid leak should therefore be as small as possible.
For tubes in good condition the effect is small but highly variable.
+20mV would be typical.

(5) Amplifier Paralysis

  The peak transient voltages during overload are greatly increased in an amplifier with feedback.
It was noted above that a short R-C time constant of the 6L6 grid coupling reduces paralysis time.
In this amplifier the effect is greatly reduced by limiting the long term 6L6 grid current by a 100k/220pF network in series with the grid.
This is not shown in the simplified circuit, but appears in the complete circuit.
When the 6L6 grid is driven positive, the grid cathode diode clamps the grid voltage at approximately 0 volts and the excess voltage appears across the 100k ohm buffer - charging up the 220pF capacitor.
The recovery time after overload is now ( 220 10-12 x 100k ) = 22uS compared with ( 47 10-9 x 330k ) = 15.5mS - a reduction by a factor of 705.
The network has virtually no effect on amplifier performance under normal operating conditions.
The low frequency impedance looking into the 6L6 grid is so high that the 100k series resistor has no effect.
At high frequencies the tube input capacity forms a capacitive divider with the 220pF capacitor.
The tube input capacity is 10pF, but this is reduced by degeneration in the cathode.
The effective cathode resistance is : 120 + 2x27 ohms shunted by the screen resistance of 8.2k = 170 ohms.
With cathode degeneration, the Gm and input capacity Cin are reduced by the factor 1 + GmRk
Here Gm = 5.5 mA/V, so the Cin is reduced by 1.935 to 5.2pF.
The capacitive divider then attenuates the high frequencies by a factor of 0.977. The turn over frequency is given by fc = 1/(2x Π x 225.2 10-12 x 105 ) = 7.06Khz.
This small effect is completely masked by the very large degree of feedback over the 6L6 output stage (>40db).
The large grid drive under overload is illustrated in the oscillogram taken with only the internal current feedback loop active.

(6) Parasitic Oscillation

  Every centimetre of conductor has its own little pico-Farad and nano-Henry, and frequently significant mutual inductance .
These may inadvertently take on the topology of a VHF/UHF oscillator around an active element.
If the gain is sufficient, oscillations build up exponentially until non-linearity in the active element limits their amplitude.
The operating point is changed and, with it, the behaviour at signal frequencies.
The output stages of vacuum tube audio amplifiers typically develop parasitics from about 50MHz to about 100MHz. Usually the tubes are driven into grid current and large biases are built up across the grid leak resistor - reducing the plate current.
The name originated in transmitter design in the early tewnties. Then grid and anode leads were long. The resulting spurious oscillation reduced the transmitter output, so they appeared to exist on the lost power and so the "parasitic" existence.
They are suppressed first by careful layout, and then by introducing resistive losses which cripple the oscillation but leave operation at the signal frequency untouched.
With vacuum tubes, the first line of defence is usually a small resistor soldered directly onto the grid tag. This forms a low pass filter with the grid input capacity, and introduces losses into any inductance in the grid circuit. In this amplifier the grid suppressors are 470 ohms.
For an input capacity of, say, 10pF this gives a cutoff frequency of 62.55MHz -- well outside the working frequency range, but at the bottom of the parasitic frequency range.
Small resistors can be introduced into the plate circuit. The large plate current in power output stages prohibits this. A small inductor is then added in parallel with the resistor - usually on the resistor's body. Modern practice is to use a few turns on a ferrite toroid with large core losses at the parasitic frequency.
Frame grid tubes such as the ECC88 are particularly prone to parasitics.
Finally it should be mentioned that one particulsr circuit configuration has a great propensity for spurious oscillation - the cathode follower.
The cathode follower has a negative input conductance for capacitive loads. This cancels out the losses in any phantom tuned circuit in the grid - usually resulting in violent VHF oscillation.
Note that the cathode followers ( V3a, V3b )( main circuit) have a 22 ohm suppressor in the grid and a 47 ohm suppressor in he plate.

(7) High Frequency Current Loop Response

 It is convenient to break up the 6L6 plate current feedback loop into three sections:-
(1) The 6L6s ( V3, V4) and their cathode load (R8, R10, R11 ).
The 6L6s on one side can be grouped together and treated as a tetrode cathode follower with an effective Gmof 2x5.5Ma/V = 11Ma/V.
 Since the screen is bypassed to the cathode, the tubes behave as tetrodes and have a very high plate resistance ( Rp ) and amplification factor ( μ).
Using Thevenin, a cathode follower has an equivalent voltage generator of [ μ/( 1 + μ )]Vin
and an output resistance of [ μ/( 1 + μ )]/Gm
Since μ >> 1 , [ μ/( 1 + μ )] ≈ 1 and the output from the cathode can be considered as Vin behind a a resistance (1/Gm) = 1/11x10-3 = 90.9 ohms.
The total cathode load is (120/2 +27 ) = 87 ohms, so the signal at the cathode of the 6L6s (Vk) is given by:-
Vk = Vin x[ 87/(87 +90.9) ] = 0.489Vin
The signal appearing across the 27 ohm resistor is then 0.1518Vin
Because of the low impedance the bandwidth is large and well outside the active range of the feedback loop.

(2) The Input Stage V2
  The input stage is an ECC82 low μ triode operating under the following conditions:-
Vp = 185V: Vg = -10.7V: Ip = 0.5Ma
Gm = 0.2Ma/V: μ = 12.5 : Rp = 62.5k
Cpg = 1.5pF: Cgk = 1.6pF : Cpk = 0.5pF.
The feedback signal from the 27 ohm sensing resistor is injected directly into the cathode. The output impedance of the phase splitter is low and prevents any of this signal appearing on the grid.
The stage therefore operates as a grounded grid stage.
The stage acts as a current generator injecting current into the grid of V2.
For a grounded grid stage the effective Gm (Gme) is given by:-
Gme = Gm [( 1 + μ )/μ][ 1/( 1 + RL/RP )]
where RP is the plate resistance and
RL is the total load (270K//1Meg = 212.6K)
So Gme = 4.91x10-5 A/V
Voltage gain = GmeRL = 10.4

(3) The Output Driver Stage V3
  The driver stage is an ECC82 low μ triode operating under the following conditions:-
Vp = 185V: Vg = -5V: Ip = 5Ma
Gm = 1.6Ma/V: μ = 15.5 : Rp = 9.69k
Cpg = 1.5pF: Cgk = 1.6pF : Cpk = 0.5pF.
The resistive load on the stage is: (27k//330k//330k)= 23.2k, so the mid-frequency gain of the stage = 10.93.
The loop gain is then given by:
Aloop = 0.1518x10.4x10.9 = 17.2
The gain reduction Afb (feedback) in the current loop is then given by:
Afb = 1/( 1 + Aloop ) = 18.2 --- (25.2db)
The reduction in gain Akr by the unbypassed 6L6 cathode resistor (87 ohm ) is given by:
Akr = 1/( 1 + GmRk )
Then Ark = 1/( 1 + 11x10-3x87 ) = 1/1.957 --- -5.83db
The total feedback over the 6L6 output tubes by the internal feedback loops is then (25.2 + 5.8)db = 31db.
The driver stage determines the high frequency loop response.
The input capacity, together with the output capacity of V1, produces a pole on the real axis. The input capacity is increased by Miller effect and the added capacity Cm is given by:-
Cm = A x Cpg = 10.9 x 1.5pF = 16.4pF.
The output capacity, together with the 6L6 input capacity, produces another pole on the real axis.
Analysis shows that the amount of feedback that can be applied to such a system without overshooot and ringing increases with the pole separation.
The steady state and transient response of the current loop without stabilisatiion is shown below:-

  HF Steady State Response :: Cfb = 0 pF
  Note: The response has a high bandwidth of about 2MHz but has a peak at about 1.7 MHz.

  Fast Step Response :: Cfb = 0 pF
The response has a fast rise time of about 200nS and overshoot and ringing corresponding to the peak in the steady state amplitude response.

  It is desirable to reduce the bandwidth of the current loop until it just sits outside the range where it starts to interfere with the stability of the main loop.
Lower bandwidths give greater freedom of layout and improve dynamic stability.
Increasing the Miller effect in V2 artificially with an external 8.2pF capacitor shifts the input pole towards the origin - thus producing greater pole spacing and stability.
Since the plate of V1 is at the same signal potential as the grid of V2, the capacitor is connected between the plates of V1 and V2 to remove the DC voltage across the capacitor.
The modified response is shown below:-

  HF Steady State Response :: Cfb = 8.2 pF
  Note: The bandwidth is reduced to about 800KHz and the peak has disappeared.
The 45 degree phase change occurs at about 400KHz - well outside the working range of the main feedback loop.

  Fast Step Response :: Cfb = 8.2 pF
  The rise time has increased and the overshoot and ringing removed.

  It is claimed above that the response of the plate current feedback loop has no significant effect on the response of the forward path of the amplifier.
The oscillogram on the right confirms this.
A 2KHz square wave is applied to the input of the amplifier with the main feedback loop open.
The input R-C low pass filter and the HF stabilisation network produce an output from the phase splitter shown on the bottom trace.
This is also the drive for the current feedback.
The plate current is shown on the top trace.
The two are identical.


(8) High Frequency Instability During Warm-Up

  A sketch of the computer model for the plate current loop is shown below:-

    Infrequently vacuum tube amplifiers, which are otherwise stable, exhibit instability during warm up.
High frequency oscillation may alter the operating conditions in one or more stages to cause a lockout, so the amplifier never reaches stability.
The mechanism of this behaviour must be understood before preventitive measures can be taken.
The trouble in almost all cases can be traced to active element synthesis of a stabilising network.
From the above diagram we see that:-
The HF stabilising network for the current loop is obtained by feedback via C4 around the active element VT2. If VT2 is inactive ( say during warm-up ), then there is still a forward path between grid and plate via C4.
The transfer function of this path is very different from when VT2 is active and may cause instability if VT1,Vt3,VT4 have become active.
Computer runs with the Gm of VT2 varied from zero to its nominal value showed that current loop was free of instability under all conditions.
Another possible position for the stabilising capacitor is shown as C14.
Since the feedback line has a much lower impedance than the plate of VT2, the effect should be minimised. Computer runs show that the stabilising effect of C14 was as expected.
Since C4 did not cause trouble and leads to more convenient wiring it was adopted.



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[B]ECC88 Cascode Input Stage

(1) Cascode Topology

The input stage consists of two triodes in cascode followed by a cathode follower.
The upper triode of the cascode operates grounded grid with a low impedance looking into the cathode, so that the gain and Miller capacity of the bottom triode is small, but usually not insignificant.
The input and output impedance are high, but the isolation between input and output is not as complete as that found in a pentode. On the other hand, there is no screen feed and decoupling to reduce the low frequency response.
The operating conditions for the two triodes in the cascode are the same:-
Vp = 75 volts: Vg = -2.2V: ip = 2.5Ma: Gm = 5Ma/V: μ = 33: Rp = 6.6K
Cgk = 3.3pF: Cgp = 1.4pF: Cpk = 2.5pF
The operating condition for the cathode follower triode:-
Vp = 150 volts: Vg = -4.8V: ip = 2.5Ma: Gm = 4.77Ma/V: μ = 33: Rp = 6.92K
Cgk = 3.3pF: Cgp = 1.4pF: Cpk = 2.5pF
If RL is the load on the cascode, the impedance Rin looking into the top cathode is:-
Rin = ( RL + RP )/ ( μ + 1 )----(1)
OR:-
Rin =[ μ/(μ +1 ) ][ 1/GM + RL/μ ] -----(2)
Now μ/(μ +1 ) ≈ 1
So for low loads RL
Rin ≈ 1/GM
This is low, the voltage gain of the first stage low, and so the Miller input capacity.

  Norton's Theorem
  If we represent the cascode stage by a current generator in parallel with a resistance, some algebra will show that the GM of the current generator is given by:-
GMNor = GM / [ GM RK ( 1 + μ)/ μ + ( μ + 2 )/( μ + 1 ) ]
and the output resistance, Rout, is given by:-
Rout = [ ( μ + 1 ) 2RK + ( μ +2 )RP
where RK is an unbypassed resistor in the cathode of the bottom tube of the cascode.
If RK = 0, that is the bias resistor is bypassed with a large capacitor then:-
GMNor = GM [ (1 + μ )/(2 + μ) ]
Rout = ( μ + 2 )RP
Since μ >> 1 , to a good approximation, the GM of the cascode is the same as that of the tubes and the output impedance is high, μ times that of the tubes.

  Thevenin's Theorem
  If we represent the cathode folower by a voltage generator VT behind an output resistance RT then:-
VT = Vin [ μ/( 1 + μ ) ]
RT = [ μ/( 1 + μ ) ] [ 1/GM ] ]
Since μ>> 1, we usually spproximate in design to:-
VT = Vin
RT = 1/GM

  Numerical Values
 Up to about 10KHz the load RL on the cascode is 60K
The cathode degeneration RK is 680//1200//3300 = 384 ohms so:-
GMNor = 1.664Ma/V
Rout = 674K
Cascode Voltage Gain = 91.7
Cathode Follower Voltage Gain = 0.967
Cathode Follower Output Impedance = 203 0hms
Overall Voltage Gain = 88.6

  Low Pass R-C Input Filter
  RF can enter the amplifier, especially if long leads are used from the preamp.
It is prudent to reject the RF in a low pass R-C filter right at the input.
Because of feedback, the grid of the input cascode may be considered to be at earth potential.
The capacity to earth is then 177pF and the driving point impedance is:-
18k//82k = 14.76K to give a cutoff frequency of 112.5KHz.

  The feedback signal is applied to the grid of the input cascode,V1a , via a compensated resistve divider ( 100k/82k ). Since the input end of the 18K resistor is usually driven from a low output impedance preamplifier, it can be considered at earth potential for the feedback signal.
On removal of the input connection from the preamp, the 47K R and 150pF C ensure that there is little change in the division ratio and stability is maintained in the main feedback loop.
The neon protects the grid of V1a from excessive voltage during warm up when using a vacuum tube preamp.



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[C]Overall Feedback Stabilisation Networks

(1)Steady State Response

  These are passive R-C networks which modify the response of the forward path so that more overall feedback can be applied with stability.
For networks which have all thir zeros in the left half plane, the phase response is a unique function of amplitude response. They are called minimum phase networks.
If the attenuation is less than 6db/octave, then the phase change is less than 90 degrees.
This means that we can get rid of gain without large destabilising phase changes.
The networks, then, have an attenuation rate less than 6db/octave between two set frequencies and are known as shelf networks.

(2)High Frequency Network

  The response of the network is shown on the right
The network is made up of the 180pF,100pF,33K,22K R-C across the 60K cascode load resistor.
At low frequencies the load on the cascode is 60K. At high frequencies the load approaches 60k//33K//22K = 10.82K
The size of the shelf is then 60K/10.82K = 5.545 ( 14.88db)
Attenuation starts at about 10KHz and, because the slope is less than 6db/octave, ends at about 150KHz.
The small decrease in overall feedback at 20KHz is considered of little consequence because of the high degree of feedback.
The topology of the stabilising network shifts the high frequency pole associated with the capacity in the cascode output.
If the output resistance of the cascode is high, the time constant for the pole on the real axis is RC (60x103) C.
But the ultimate load is 10.82K, so the pole now has a time constant of 10.82x103C - a much higher cutoff frequency - which removes it beyond the active frequency range of the overall loop.


(3)Low Frequency Network

  The response of the network is shown on the right.
It consists of the 6.6Meg, 1.8Meg, 680K, 470K resistors and the four 0.1uF capacitors. It also provides DC isolation between the cathode follower, V3a, and the grid of V5a.
The corrective shelf starts at about 20Hz and continues down to about 1Hz. with a phase change of about 70 degrees.



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[D]ECC88 Phase Splitter Stage

(1)Operational Amplifier

    The phase splitter should have a flat and stable gain near unity and a phase change very close to 180 degrees over the working frequency range of the amplifier.
An operational amplifier with high gain fulfills both requirements.
For the ECC88s in the cascode:-
GM = 5Ma/V : μ = 33 : RP = 6.6K
Since the cathode is bypassed with a 4700uF capacitor RK = 0
From the equations above, we get the Norton equivalent for the cascode:-
GM = 4.854Ma/V : Rout = 231K : RL = 60K.
So voltage gain A = 231.
The cathode follower gain = 0.967 to give an overall gain of 223.7.
The feedback network has a gain of 0.5 to give a forward loop gain of 112.

(2) Balance Adjustment

    Both the quiescent operating conditions and gain of the 6L6 output tubes are under heavy feedback [ ≈ 31db or x35.5 ]
The balance of the push-pull output stage is then virtually independent of the output tubes.
Only a small adjustment in the phase splitter gain is necessary for perfect overall balance.
The total 6L6 output current is summed in a 1 ohm common resistor.
For perfect balance there is no signal across this resistor.
To balance the amplifier apply a 2KHz square wave to the input.
Adjustment of the 3/27pF capacitor brings the front to zero and the 100K pot. brings the top of the wave to zero.
The adjustments do not interact and give easy convergence.


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[E]Overall Feedback Loop

(1) Output Transformer Response

    The output transformer uniquely determines the response of the forward path.
A transformer driven from a high impedance has two dominant high frequency poles - one formed by the self capacity of the primary winding and the other by the primary-secondary leakage inductance.
The primary inductance and reflected load form a low frequency pole.
Due to the iron core, the primary inductance is highly non-linear. This non-linearity manifests in two ways:-
    (1) The inductance varies with signal level.
It is small for low levels - rises to a maximum ≈ 800H and then falls off as the core saturates.
The low level inductance is also a sensitive function of any DC bias current due to unbalance in the push-pull output.
For high levels the magnetising current is far from sinusoidal and the usual definition of inductance breaks down.
If the low frequency stability depends on transformer response, it is possible to imagine an amplifier starting low frequency oscillation at a low level and then the level stabilising as the amplitude builds up.
    (2) Driving the transforner primary from a zero impedance source will still result in distortion.
The non-linear voltage drop across the primary resistance caused by the non-linear magnetising current presents a distorted internal drive voltage.
The overall feedback, then, must come from the secondary.
The output stage supplies both the load and magnetising current.
As the magnetising current increases, the maximum available load current decreases, and so limits the power output from the amplifier at low frequencies.

(2) Stabilising Strategy for High Frequencies

    We can get a very rough estimate of the position of the two high frequency poles asscociated with the output transformer:-
  POLE 1 :-   Formed by the primary winding capacity ≈ 500pF and the reflected load 3500 ohms.
    Τ = RC = 500x 10-12 x 3500 = 1.75x10-6 :: fc = 1/( 2 Π Τ ) = 168KHz.
  POLE 2 :-   Formed by the primary seondary leakage inductance ≈ 10.76mH and the reflected load 3500 ohms.
    Τ = L/R = 10.76 x0-3 / 3500 = 3.09x10-6 :: fc = 1/( 2 Π Τ ) = 95.6KHz.
Analysis shows that a forward path with two poles this close will tolerate little feedback before developing a peak in the steady state response and severe ringing in the transient response.
Two stratigies are adopted to overcome the problem:-
[A] Up to about 40KHz, feedback is derived from the transformer secondary. Beyond this frequency, feedback reverts to the primary, reducing the transformer to a one pole system.
[B] A shelf is introduced into the forward path which starts to introduce attenuation from about 10KHz

(3) Stabilising Strategy for Low Frequencies

  For normal operating levels, the transformer low frequency cutoff is given by:-
Lpri ≈ 800H : RL = 3500 ohms : Τ = Lpri / RL ≈ 0.229S : fc = 1/( 2 Π Τ ) = 1.29Hz.
The lowest audio frequency applied to the amplifier is estimated as 20Hz, so the low frequency shelf was designed to attenuate between 20 and 1 Hz.
This gives a large phase margin to accomdgate any decrease in inductance at low levels.
The cutoff frequencies of the plate current loop, the phase splitter, and the cascode input are below 1Hz , so do not affect stability.

(4) Feedback Network Around Transformer

  Suppose we connect a capacitive voltage divider to the primary of the transformer and a resistive voltage divider to the secondary.
Make the division ratio of the capacitive divider equal to the transformer division ratio by the resistive divider ratio.
If the transformer is ideal, the voltage output from both dividers is identical - so their outputs can be joined.
At high frequencies the impedance of the capacitive divider falls below that of the resistive divider, so it wll predominate.
The primary voltage determines the output from the network at high frequencies, and so the extra pole associated with the primary - secondary leakage inductance is eliminated from the forward path.
The turnover frequency is easily calculated using Thevenin.
The output capacity of the divider is the sum of the two capacities: the output resistance of the secondary divider is given by the two resistors in parallel : the time constant is the product of the two.
The above plot shows the steady state response of a current driven transformer surrounded by a network with a cutoff frequency of 37.4KHz
Note: The ultimate slope of the primary and network voltage is 6db/octave and the secondary 12 db/octave because of the extra pole.
The ultimate phaase change of the primary and the network is 90 degrees, while the secondary goes to 180 degreees.
The transfer function of the transformer is not a constant as assumed, but is modified by the leakage inductance.
This causes a dip in the response of the network at about 30 KHz.
This network is in the feedback path - not the forward path. This results in a corresponding peak in the overall response.
Computer runs show that an increase in the "top" capacity will very nearly eliminate the dip, so the capacitor is made adjustable.
Setup is simple:- The front of the square wave output is adjusted for best response.
The bottom resistor of 665 ohms is replaced by a 1.8K, 180 ohm and 1K adjustable potentiometer. This allows the convenient removal of the overall feedback for test and fault finding.
The change in the network response as capacity is added to the "top" capacitor is shown in the following computer runs.

  Note that for trim Cs from about 10pF to 15pF the primary response and the network response are very close.

  When the added trim C is correctly adjusted the front of the step response looks like this.
Note:-Low level ringing at about 67KHz sometimes turns up in the test results, but not in the computed waveforms.
Approximations in the computer model for the output transformer cause this.
Some of the approximations are:-
(a) The winding capacity is distributed, not lumped.
(b) The resistance of the windings is not constant, but increases with frequency due to skin and proximity effect.
(c) The resonant frequency of each half of the primary winding is different.

    Overall ( Closed Loop ) Steady State Response
The response from the transformer feedback network is also shown.
The feedback keeps this response relatively flat.
The dip in the response of this network at about 40KHz with Ctrim = 0 results in a peak in the overall response.

    Overall ( Closed Loop ) Steady State Response
The response from the transformer feedback network is also shown.
The feedback keeps this response relatively flat.
With Ctrim = 12pF the difference between the feedback network and transformer output is greatly reduced, so the output is also flat.

(5) Open Loop Transfer Function

    The open loop transfer function is shown below in Cartesian (Bode) and polar ( Nyquist ) form.

    The open loop response reaches unity gain at a frequency of about 280 KHz. and a phase change of 110 degrees. This indicates a phase margin of 70 degrees - a stable amplifier with little ringing in the transient response.

    The same information but in polar form.
I have found this form more useful in setting exam questions than in designing practical feedback systems.

(6) Return Difference

    A plot of the return difference in the overall loop is shown opposite.
The magnitude of the return difference gives a measure of the reduction in distortion.
The return difference is 22db ( x12.6) up to about 5KHz falling off to 18db (x7.9) at 20KHz.
This reduction is considered of little consequence, since the total return difference on the 6L6 output stage from current feedback is 31.2db (x36.5).


(7) Output Impedance

    The amplifier output impedance with the overall loop closed (LHS) amd open (RHS).

    The output impedance is measured looking into the amplifier terminals setup to drive a 4 ohm load.
It is low (0.34 ohms) and purely resistive up to about 5KHz.
By 20KHz it has become purely reactive with a magnitude of 1 ohm. This represents an inductance of about 8μH.

    Since the primary of the output transformer is driven by a current generator, the low output impedance depends entirely on the overall feedback loop.
To demonstrate this, the output impedance is calculated with the loop broken.
As expected, the impedance of an open circuit transformer turns up.
The primary winding capacity resonates with the primary inductance to give a peak at 256 Hz.
The primaey capacity and primary - secondary leakage inductance form a series tuned circuit at 68KHz.


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[F] Transient Response

(1) Drive from Input Cascode and Phase Splitter

    It is interesting to study the waveforms through out the amplifier for a step function input.
A step with a very fast front will overload the input stages of a feedback amplifier.
The low pass R-C filter at the input to the amplifier will slow the front down and prevent this.
The response of this filter is given by:-
Vo(t) = 1 - e-t/τ where τ = 2.21μS
This was used as the input waveform in the computer program

    Computed Result
    The input cascode stage and the current feedback loop are high bandwidth, so that there is a very fast path from the input grid to the transformer primary.
This is indicated by the sharp front on the phase splitter output.
This sudden rise in current charges the primary capacity and causes the steep initial slope on the primary voltage.
The primary - secondary leakage inductance forces the secondary to have zero slope at t = 0 and a slower rise time.

    Test Result
    The CRO time base is about half the speed of the computed result, but the two are in substantial agreement.

(2) Feedback Network and Output Waveform

    Computed Result
    This is a good illustration of the addition of the fast front of the primary and the long tail of the secondary to give the output from the feedback network.
Since this signal is applied directly to a compensated voltage divider to generate the error signal, it is forced by feedback to be very close to the input.

    Test Result
    The output waveform into a resistive load at about half power output.
The fronts are clean, the ringing minimal, and tops are flat suggesting good low frequency response.

[G] Low Frequency Considerations

(1) Some Basic Formulae and Constants

   It is interesting to evaluate some of the pressures in a sound wave:-
  At standard temperature, atmospheric pressure p = 105 N/M2
 Density ρ = 1.18 Kg/M3
  Velocity c = 344.8 M/S
  Characteristic impedance Zo = ρ c = 406.86 ohms
  Intensity I = p2/Zo = p2/(ρ c ) W/M2 ----(1)
  The intensity for 0db reference level ( threshold of hearing ) is defined as: I = 10-12 W/M2
  Substituting in (1) above we have pref = 2x10-5 N/M2
  If the level rises to 100db, the sound pressure is still only 2 N/M2 on top of 105 N/M2 - still a very small perturbation of atmospheric pressure.

 Audio channels are inherently AC coupled

 It is important to retain the light level in a scene, so video channels are inherently DC coupled

(2) AC Coupled Systems

    Rise-time, overshoot and ringing associated with the high frequency response are well known - sag and droop, the low frequency transient parameters, less so.
A few of the salient features of low frequency transient response theory are now outlined.

(3) Sag and Droop

   If the step response of an AC coupled system is normalised to 1, then the negative of the slope immediately after the step is called the "SAG" S.
The time just after the step is designated as t = 0+
The definition of "DROOP", D, for a square wave is given opposite.
The relationship between the two is given by:-
S = 4 f D
where f is the frequency of the square wave.


(4) Low Frequency Transfer Functions

    The sag S can be extracted from the low frequency transfer function.
It can be shown that:-
S = Lt [ p( YN(p) - 1 ) ] as p--> ∞
where YN(p) is normalised to give unit step output.
The normalised transfer function of an R-C coupling network used in the amplifier is given by:-
YN(p) = τp/( 1 + τp )
so for this network the sag is given by:-
S = Lt p[ τp/( 1 + τp ) - 1 ] as p --> ∞
ie S = 1/τ
If we expand the normalised transfer function into a series we have:-
YN(p) = 1 + a1/p + a2/p2 + a3/p3 . . . . . . .
where the first term is 1 because the transfer function is normalised.
If we evaluate sag we have :- S = Lt p[ 1 + a1/p + a2/p2 + a3/p3 . . . . - 1 ] as p ---> ∞
ie S = a1
If we put a number of systems in cascade then the we multiply the series representing each transfer function and the first term coefficients add.
We then have the useful result:-

 The sag of cascaded channels adds algebraically

Since we can design networks with sags of opposite sign, equalisation of the slow speed transient response is easily accomplished.


(5) Low Frequency Small Signal Square Wave Response

    The small signal square wave response at 20Hz is shown opposite.
This indicates an excellent response with a droop of about 0.17. It is the response predicted by the linear theory used to design the amplifier, and also the response given by the small signal computer program.
The peak flux densities in the iron of the transformer core increase inversely with frequency and eventually enter a highly non-linear region at some low frequency.
This results in a change of wave shape and the distortion illustratred below.


(6) Effect of Magnetising Current

   The effect of non-linear magnetising current is shown below:-

Low Level Output at 20 Hz.

Near full output at 20Hz.

Near full output at 50Hz.

  The change in waveshape with output level at 20 Hz is illustrated below:-
The Y (voltage) scale is as follows:-
[1] 500mV/div
[2] 1Vdiv
[3] 2V/div
[4] 5V/div
[5] 10V/div
[6] 5V/div

  The increase in peak magnetising current with increase in output at 20Hz. is illustrated below:-

The upper trace (yellow) is the plate current drive with zero DC on the x axis.
The lower trace (blue) is the voltage across the resistive load.

  The decrease in peak magnetising current with increase in frequency is illustrated below:-
The frequencies are:-
[1] [2] [3] 20Hz
[4] 50Hz.
[5] 80Hz.
[6] 100Hz.

(7) Distortion of Low Frequency Sinusoids

   The magntising current for sinusoidal outputs is shown below:-
Frequency:-
[1] 12Hz.
[2] 13.5Hz.
[3] 20Hz.
[4] 50Hz.
[5] 80Hz.
[6] 100Hz.
Note that the output waveform at 20 Hz. looks clean although the transformer prinary current has a kink.


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[G] Amplitude and Phase Response

(1) Final Tests : Steady State Amplitude and Phase

    The steady state response should indicate that the amplifier is flat and phase linear over the working frequency range.
The test results given below show that this has been achieved.

    Amplitude Response
    The amplifier is flat down to 10Hz, but the power output at this frequency is restricted by the magnetising current of the transformer.

    Phase Response
    The amplifier is phase - linear over the working range.
This implies signal delay, but no transient errors.


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[H] Distortion

(1) Final Tests : Harmonic and Intermodulation

    The distortion is at the limit of the test equipment.
New gear has been designed to extend the limit by several orders of magnitude.
The distortion level is way below audibility, so the results are of interest to confirm the design ideas but little else.


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