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Where TMC really shines: a novel transimpedance stage (TIS).

Note: This page will be updated from time to time (and press F5).
How to get rid of the cons and keep the pros of both techniques

We can improve the performance in two ways: either by decreasing  
the load on the VAS in case of TPC, or by decreasing the load on the  
IPS in case of TMC . Let's start with TPC. This can be realized by  
using the emitter of the (pre-) driver as take-off point for the Miller  
compensation, together with a small load on the VAS output itself,  
similar as depicted by fig.3b.  But there's another (minor) issue with  
TPC not previously discussed here. Inherently to this kind of second  
order compensation, the step response suffers from a noticeable  
amount of overshoot. Although it can be remedied by an additional  
lead-lag compensation as has been shown by Megajocke, yet there  
are two more problems with complementary TISes: The stability of  
VAS quiescent current and the so called fighting VAS issue. These  
can be remedied by a common mode control loop (CMCL). However,  
the added complexity makes this route less attractive. So let's see  
what TMC has to offer.
As said before, in this case the load on the IPS has to be decreased,  
which can be realized by applying a so called 'Input Inclusive  
Compensation'. Instead of connecting the Miller cap C1 to the TIS  
input, just tie it to the inverting input of the IPS.  Now, the IPS has far  
less work to do: Only supplying current to the TIS instead of supplying  
current to the compensation capacitor as well, which is normally one  
order higher. See fig.4, upper curves, OMC versusTMC-2.
However, this not without consequence. Not only the Miller ULGF  
becomes way too high, but also the phase shift from the IPS adds to  
the Miller loop beyond an acceptable level. To maintain sufficient  
stability a redistribution of gain stages is required    This is done by:
Fig.5  Barebone implementation of the Super TIS. THD20k = 51ppb.
Fig. 6  Implementation of the Super TIS including input LP filter, cascodes and pre-drivers.
References:

John Ellis, "Audio Power Amplifier Frequency Compensation"  Electronics World, March 2003.

Dimitri Danyuk, "On the Optimization of Enhanced Cascode", AES paper, October 2008.
http://www.aes.org/e-lib/browse.cfm?elib=14723

Harry Dymond & Phil Mellor, "Analysis of Two-Pole Compensation in Linear Audio Amplifiers", AES paper, November, 2010
Paper can be downloaded here.

Malcom Hawksford, "Reduction of Transistor Slope Impedance Dependent Distortion in Large-Signal Amplifiers.",
J. Audio Eng. Soc., Vol. 36, No. 4,  1988 April.   Paper can be downloaded here.

Megajocke, Calculation of the additional lead-compensation to correct the step response of TPC:
http://www.diyaudio.com/forums/solid-state/171159-bob-cordells-power-amplifier-book-122.html#post2414320

Bod Cordell, 'A MOSFET Power Amplifier with Error Correction', Journal of the Audio Engineering Society Vol. 32, January 1984
Paper can be downloaded here.










Circuit Description

Why cascodes
Under perfectly balanced conditions of the IPS the Early effect and nonlinear Cob don't affect the performance. In that case there is no need for cascodes.  
However, we do not always know the output impedance of the pre-amp to which this circuit is connected and if we know, it's a bit cumbersome to adjust R1 to  
the right value. Keeping Vce constant by means of cascodes avoid these issues.Opposed to the first circuit, varying R1 from zero to 400 Ohms has hardly any  
effect on the distortion.

Bias Q13 & Q14
Q13 and Q14 need some bias current, of course. This current, defined by R22,  not only depends on the supply voltage, but it also subtracts from the TIS  
standing current. It's the latter we don't want. Therefore R21 is added to compensate for this dependence. Now, any current substracted from the TIS is at the  
same time added to the TIS via the current mirrors, giving a net result of zero deviation.

Taming the super pair
Due to positive feedback of the base currents, Baxandall super pairs tend to be unstable. This becomes apparent by some peaking of the gain at tens of MHz  
when the TIS output isn't loaded by any shunt compensation. Capacitors C10 and C11 diminish the amount of positive feedback to a safe level and prevent  
oscillations at high frequencies. With the shunt compensation in place however, the peaking has also gone. Nevertheless, I have kept C10 & C11 to be on the  
safe side.

Input Low Pass Filter
The objective of this filter is twofold: Preventing HF ingress and limiting the slew rate. As this front-end is intended to drive a MOSFET OPS some caution is in  
order. The higher the SR, the higher the gate currents and the higher the stress on the drivers. So reducing the SR from 500V/us to 50V/us (that's more than  
adequate for an audio amp) will also reduce the peak current of the drivers by a factor of ten. As a result, one can use smaller (and faster) drivers. A second-
order filter is used as this one, in contrast to a first-order filter, limits the SR far better at the onset of a large and steep impulse. Since this is the moment  
where Vce of the drivers is at it highest, such filter does a better job of limiting the current as well as the power dissipation (courtesy of Andy Connor).

TMC
As the first circuit lacks some Miller loop gain, this has been remedied in the second circuit by including the pre-drivers into the  Miller loop. See C16 and C17  
which are connected to the emitters of Q19 and Q20.  But leaving the TIS output unterminated  (with a capacitive load) is not a good idea, as the HF response  
will be ill-defined (mainly by parasitic stray capacitances). In order to define and limit the gain at HF, the TIS output has to be terminated by some capacitve  
load, in effect shunt compensation. However, a simple (first-order) shunt compensation would decrease the loop gain at audio frequencies too much again. So  
I have opted for a second-order compensation.  At HF the compensation is defined by  C12 ... C15 & R26, while at AF it has hardly any effect, as the whole  
network is bootstrapped by the pre-driver emitters via R27 & R28.

Bootstrapped collectors of the pre-drivers
Since the TIS exhibits an extreme high output impedance (that is, without frequency compensation), it is very sensitive to the nonlinear Cob of the pre-drivers.  
As a matter of fact, it would put the whole project in peril. This can be avoided simply by bootstrapping the collectors of the pre-drivers, see C18 & C19.

Some Specifications
THD20k at Vi = 1.47V-pk: 61ppb, mostly 2nd and 3rd harmonics and independent of Ri (within certain limits, of course).
THD200k at Vi = 1.47V-pk: 3.1ppm.
Slew Rate without input filter: max. 500V/us.
With input filter: Tr = Tf = 1.6 us (slew rate is meaningless).
Filter cut-off frequency: 290kHz.
Max. output voltage at node out: +/- 47.5V;
Max. voltage at node A: +49V. Thus almost rail to rail.
BTW, the front-end of Bob Cordell's EC amplifier, a non-complementary design of the same complexity, distorts 1ppm at 20kHz.
Some practical implementations of the Super TIS

Fig.5 shows a simple, but fully complementary symmetrical  
implementation, which also incorporates two Baxandall  
super pairs. If single transistors were used instead of super  
pairs, the low distortion of the IPS would have been  
completely swamped by the distortion of them.
Although the current gain of the TIS is just 0dB,  the gain-
bandwidth-product of the stages enclosed by the Miller loop  
is still too high. Therefore, a so called PLIL compensation  
(C1 & R7) is added to stabilize the Miller loop. See John Ellis  
for more information on this subject.
By the way, many other configurations also need additional  
compensation to tame the Miller loop.
Since the VAS has been replaced by a cascode having a  
current gain of just 1x, another problem arises:  Any load  
(including C2) at the output of the TIS will also been 'seen' by  
the IPS. At first sight not much seems to  be gained by this  
circuit. But... this is where TMC comes into play (and  
shines!), as it moves the capacitive load from the TIS to the  
OPS, well, at least at frequencies of interest. In this way  
(differential) collector currents of the IPS are greatly reduced.  
Compared to TPC at 20kHz by a factor of about 20 and  
compared to OMC by a factor of about 4 (of course,  
depending on circuit details).
For the same reason THD20k is much lower with TMC:  
51ppb, leaving TPC (C2 & C3 not swapped) in the dust  
with an embarrassing 1.3ppm.
It should be noticed that the current gain and gm are still  
rather low. Ignoring second order effects (finite beta, etc.)  
they are approximately: gm ~= 2 / ( RE + VT / Ic )  
= 2 / ( 10 + 26 / 2.5) = 98 mA/V (simulated: 94 mA/V)
Iout / Ifb ~= Rfb*gm = 200*0.098 = 19.6 (simulated: 17.4).
Therefore, it's highly recommended to compensate for the  
lack of gain by means of a pre-driver.
Fig. 7  Gain and phase response of the internal Miller loop (gain probe put between C9 and R25),  which shows a healthy gain  
margin of 13dB respectively 96 degrees phase margin. The phase dip at 1MHz is due to the dual pole shunt compensation.
A welcome side effect of a TIS gain of just 1x is that  you don't need a CMCL to define the quiescent  current of the TIS (that saves 4 to 6 transistors).   
Instead, it's defined by the tail current of the IPS. More precisely, it's just equal to the tail current.
On the other hand, the limited gain has a marked effect on the effectiveness of TMC in reducing the distortion of the OPS: As the reduction is based on  
increasing the loop gain, it is only effective if there is enough gain 'in reserve'. Without a 'surplus' of gain the distortion from the OPS will not or hardly be  
lowered by means of TMC.
Another point of concern is an increase  in THD when the inputs of the IPS don't 'see' equal impedances. If, for example, R1=0 then THD20k = 212ppb and if  
R=400 then THD20k = 123ppb. These issues will be remedied in subsequent implementations.
Fig.8. Clipping behavior at 20kHz from amp fig.6.
What we have gained                                                                           

One may ask what we have gained with the Super TIS. Well, a lot. Let's  
compare it to a more traditional approach of a full fledged symmetrical  
front-end, i.e. one with IPS- and VAS-cascodes, a CMCL, protection of  
the VAS and provisions for an active clamp, see above, fig.9.

First, it uses almost twice as much components. Second, the  
performance lags far behind. Using TMC, the distortion at 20kHz is more  
than ten times higher and the maximum slew rate five times lower.  

Using TPC with the same capacitors (fig.10) THD figures do improve,  
though not to the same level as the Super TIS. The slew rate however,  
dropped to 46V/us and the step response looks ugly.

With swapped TPC capacitors (fig.11, courtesy of Harry Dymond) THD  
figures come close to the performance of the Super TIS, though the  
slew rate still lags behind with 184V/us versus 500V/us of the Super TIS.

By the way, who says that the TPC capacitor ratio (C21:C13) is totally  
irrelevant?  

While the circuit of fig.9 needs VAS protection (by means of Q23 &  
Q24), the Super TIS doesn't need that, as it's self-limiting (governed by  
the LTP current sources).
Fig.9. A fully symmetrical front-end using more traditional techniques and complemented with a CMCL to stabilize the VAS current. By now totally obsolete!
Fig. 10. Two Pole Compensation (TPC)     Fig.11. Ditto, with swapped caps
Fig.12. The Super TIS integrated with an Auto Bias-II Output Stage and a current limiter (at 30A).
Introduction
The objective of this project is the realisation of a simple low cost yet symmetrical and ultra low distortion front-end suitable to drive high-end audio output
stages (for example this one). In addition, providing a high PSRR and a (near) rail to rail ouput swing, which makes an elevated and heavily filtered supply
voltage for the front-end unnecessary. Low distortion is obtained by using so called 'Baxandall super pairs' as well as Transitional Miller Compensation.

Acronyms
Ai:           Current gain
Av:          Voltage gain
Cdom:    Dominant pole compensation capacitor or Miller capacitor
CMCL:    Common Mode Control Loop
gm:         (mutual) Transconductance
IIC:          Input Inclusive Compensation
IPS:        Input Stage
LTP:       Long tailed Pair
OMC      Ordinary Miller Compensation
OPS:     Output Stage
PLIL       Phase Lead, Input Lag (compensation)
PSRR    Power Supply Rejection Ratio
SR:        Slew Rate
TIS        Trans-impedance Stage (also called VAS)
TMC      Transitional Miller Compensation
TPC      Two Pole (Miller) Compensation
ULGF     Unity Loop Gain Frequency
VAS        Voltage Amplification Stage (also called TIS)
OMC versus TPC versus TMC

A common way to explain the improvement from TPC or TMC over  
OMC is to look at the increased loop gain. The higher the loop gain,  
the lower the distortion. As simply as that. In case of TPC, all stages  
(IPS, VAS, Driver & OPS) are exposed to the increased loop gain,  
while in case of TMC the IPS doesn't benefit from the increase loop  
gain. So, one might conclude that TPC is superior over TMC.  
Theoretically, yes. Practically, certainly not in every case, as has  
been revealed by simulation of practical circuits. These seemingly  
contradictory results have led to a heated debate on DIY Audio  
Forum, which started here and continues there.

Clearly more factors are involved than just loop gain. Hence, a  
different approach is needed to fully explain the effects of TPC and  
TMC on  distortion. So, let's have a look at the load on the output of  
the IPS and VAS, because the lighter the load, the less distortion.  
Again, as simple as that. In the next simulations (of a typical  
mainstream amp) the load is expressed as AC current at a constant  
sine input signal of 1V. Four cases were investigated: OMC, TMC  
and two versions of TPC. I1 is the IPS output current and I2 is the  
VAS output current. See fig.1.

What we see, as expected,  is that I1 is much lower in case of TPC,  
while in case of TMC, I1 is about the same or slightly higher  
compared to OMC. So far so good and in accordance with the  
textbooks.  I2 however,  shines a different light on these  
compensation schemes. See fig.2, bottom graphs. Now it is TMC  
that reduces the VAS loading by almost an order of magnitude, while  
TPC, if correct implemented (fig.1b), slightly increases the loading.  
However, if C1 and C2 are swapped (TPC-wrong), the VAS loading  
increases by an order of magnitude, resulting in much higher  
distortion. Needless to say that the latter is not recommended.
Fig. 2.   AC currents as function of frequency seen at the output of the input stage and VAS output for different compensation schemes.
Pros and Cons in Summary
TPC reduces distortion of IPS, TIS and OPS as well, though it puts a higher load on the TIS output.
TMC only reduces the distortion of the TIS and OPS. However it decreases the load on the TIS output.
As both techniques have their pros and cons, practical implementations in power amps will yield similar improvements and there's no clear winner.






Fig.3a. Modified Transitional Miller Compensation enclosing the input stage.
Fig.3b. Ditto, enclosing the pre-driver as well.
Fig. 4.   AC currents as function of frequency seen at the output of the IPS and VAS (or TIS) output of fig.3a and 3b.
Fig.1a: Ordinary Miller Compensation; 1b: Two Pole Compensation; 1c: Transitional Miller Compensation

Effects of RF Ingress

It is said that a JFET input stage not just produces less distortion but also it is less susceptible to RF ingress. So I was curious whether this claim holds for   
the SuperTIS as well.  To find that out four different front-ends were subjected to analysis (that is, simulation):
1. A SuperTIS with a BJT input stage.
2. A SuperTIS with a JFET input stage.
3. The front-end of Bob Cordell's HEC MOSFET amp with a BJT input stage.
4. The front-end of Bob Cordell's HEC MOSFET amp with a JFET input stage.

First, an AM demodulation test was performed using a 1V 10MHz carrier, modulated by a 20kHz sine with a modulation depth of 70%. The 20kHz component  
at the output of the front-end was then 'measured' by means of an FFT.  

Next, a 10MHz sine also of 1V amplitude was superimposed on an AF signal of 1V and 20kHz. This was done to figure out how much the HF signal  
contributes to distortion of the AF sine. Since a strong HF signal not necessarily will lead to AM detection, it may nevertheless push the audio signal into a  
nonlinear region. As a result, compression of the audio signal will take place. Hence a 'compression test' has been included as well.

Front-end:               SuperTIS-BJT   SuperTIS-JFET   HEC-BJT   HEC-JFET
Demodulated AM signal:      0.73mV         10.1mV       1.52V      1.27V
THD20k without HF carrier:  0.028ppm       0.071ppm     0.19ppm    0.76ppm*
THD20k with HF carrier:     0.656ppm       457ppm       161ppm     156ppm
THD20k increase:            0.628ppm       457ppm       160ppm     155ppm

These figures clearly indicate that the SuperTIS will not benefit from JFETs in the input stage.
Needless to say that in every respect the BJT version of the SuperTIS is the winner.

After a second thought, above enormous discrepancies between BJT and JFET results made me suspicious. So I decided to repeat the simulations with a  
smaller HF signal. This time of 100mV instead of 1V.  Now we get a totally different picture:

Front-end:               SuperTIS-BJT   SuperTIS-JFET   HEC-BJT    HEC-JFET
Demodulated AM signal:      5.4uV          1.26mV       0.35mV      0.82mV
THD20k without HF carrier:  0.028ppm       0.071ppm     0.19ppm     0.76ppm*
THD20k with HF carrier:     0.030ppm       0.072ppm     0.24ppm     26.3ppm
THD20k increase:            0.002ppm       0.001ppm     0.05ppm     25.5ppm

These differences are far less extreme. Still, BJTs yield better results in both cases and the SuperTIS still outperforms the other front-end.
For further reading on this topic look hereherehere and here at the diyAudio forum.

* This figure reduces from 0.76ppm to 0.23ppm if the input cascode (Q2 & Q6) is bootstrapped.

Below are the test circuits for RFI simulations.
Fig.13. RFI test circuit of SuperTIS plus BJT input stage.
Fig.14. RFI test circuit of SuperTIS plus JFET input stage.
Fig.15. RFI test circuit of Cordell's HEC-MOSFET amp plus BJT input stage.
Fig.16. RFI test circuit of Cordell's HEC-MOSFET amp plus JFET input stage.


Fig.17. SuperTIS combined with the Hawksford-Cordell error correction output stage
Out of curiosity,  I tried to combine the SuperTIS with Bod Cordell's HEC output stage. In a first attempt,THD figures were not that encouraging: Three to four  
times higher than obtained by the original amp of Bob. This was due to the nonlinear loading on the TIS ouput by the pre-drivers (Q21 & Q22). After adding  
Q19 & Q20, thus forming a diamond buffer together with Q21 & Q22, results were much better. With optimally tuned resistors R25 & R26, I got THD20k =  
3.1ppm compared to 4ppm from the original amp. With TMC enabled (R23=2k2 instead of infinity),  the distortion dropped to 0.77ppm.
Fig.12a.  Global gain and phase response (gain probe put between R19 an node FB.)
Fig.12b. Input gain and phase response (gain probe put between base of Q12 and node FB)
Fig.12c. Output gain and phase response. Look here to see how and where the gain probe has been put.
Fig.12d. Auto bias differential (i.e. error correction) gain and phase response
(gain probe put between output and basis of Q30, Q31, Q33 & Q34)
Fig.12e. Auto bias common mode gain and phase response (gain probe put between R63 and R72)
This loop controls the quiescent current of the output stage.
Fig.12f. Gain and phase response of the output current limiter @ Vi = 1.4V and RL = 1 Ohm (gain probe put between Q53 and R71)
NB: The phase dip at 400kHz is due to the inductor of the Zobel network.
Fig.12g. Closed loop gain and phase response simulated before the Zobel network.
Fig.12h. Closed loop step response simulatd before the Zobel network.
Fig.12i. Harmonic distortion at 20Hz. 200W into 4 Ohms. Green = fundamental, black = residual
(notice the multiplier 1E7), blue = harmonic components, red = THD (full scale = 0.1ppm)
Fig.12j. Harmonic distortion at 200Hz. 200W into 4 Ohms. Green = fundamental, black = residual
(notice the multiplier 1E7), blue = harmonic components, red = THD (full scale = 0.1ppm)
Fig.12k. Harmonic distortion at 2kHz. 200W into 4 Ohms. Green = fundamental, black = residual
(notice the multiplier 1E7), blue = harmonic components, red = THD (full scale = 0.1ppm)
Fig.12l. Harmonic distortion at 20kHz. 200W into 4 Ohms. Green = fundamental, black = residual  
(notice the multiplier of 1E5), blue = harmonic components, red = THD = 1.5ppm  (full scale = 2ppm).  
Owing to a  third order compensation scheme, the amount of feedback decreases with the third  
power of frequency. Hence the larger harmonics at higher frequencies.
Fig.12n. Clipping behavior at Vi = 2V and f = 20kHz. Since no provisions are made  to limit the output
voltage to a predetermined value (for example by means of a Baker clamp), some 'sticking' is visible.
Fig.12o. The short circuit protection in action at Vi = 1.4V,  f = 20kHz and RL = 1 Ohm.  Blue = output voltage, red = MOSFET
total drain current, limited at 31A.  This figure was obtained without Zobel network. Including the Zobel will result in some ringing.



Fig.12m. ITU-R intermodulation test with two sine waves of 19 and 20kHz (green). Blue = individual IM products, 
blue = RMS value of IM products. Total IMD = 0.047ppm at BW = 18kHz (full scale is 0.05ppm).
Fig.12p. The 'R.C. Bowes stability test'.  A small 250kHz square wave is superimposed on a large 10kHz sine
wave. In this away instabilities at many different output levels are easily detected.  Near clipping some ringing
occurs, see red detail. Notice that for this test the input filter has been disabled.
Fig.12q. Stability test during the power-on phase. Supply voltage was stepped from 3 to 10V. Input signal was a 20mV  
20kHz square wave. The upper graphs show serious ringing, caused by saturation of the pre-driver transistors Q21 & Q22  
at low supply voltages. Bootstrapping the collectors by means of D16 & D17 cured the instability, see lower graphs.
Fig.12r.  DC collector and drain current during start-up. Power supply voltage has been varied from 0 to 60V. Red = total drain  
current of the MOSFETS * 10. Green = Ic of the drivers. Between 3 and 25V it's slightly higher, as bootstrap current is also  
supplied to the pre-drivers. Violet = Ic of the TIS. Black = Ic of the pre-drivers. Blue = output voltage, which stays very close to zero.
Home
 
1. Replacing the ubiquitous VAS (with a gain of beta or even beta^2)  by a cascode (with a current gain of 1x) which is directly connected to the current mirror,

2. Putting a pre-driver after the cascode, which restores the gain of the whole chain, see fig.3a.

The cascode comprises not just a single transistor, rather a Baxandall super pair. As a result, the distortion caused by the nonlinear Cob and Early effect has  
been almost completely eliminated. See Dimitri Danyuk and Malcom Hawksford for more information.

A futher improvement can be obtained by tying the compensation capacitor C2 to the output of the next stage, i.e. the pre-driver, see fig.3b. In this way, IPS and  
TIS output currents are reduced by almost three orders of magnitude, see fig.4 TMC-3.