Aleph Bet is a single stage, single ended, unity gain, line level buffer that can drive a 2kOhm load with vanishingly low distortion.
It uses a composite transistor known as the Baxandall Super Pair (see the attached 1966 article) in the follower role with an Aleph current source (as described in the attached patent by @Nelson Pass) as its load, hence the name. A few twists have been added to that general theme and can be glanced from the simplified schematic:
The distortion performance is quite good (note that this buffer has distortion well below that of the ADC, so the fundamental is suppressed after the buffer and before the ADC in order for the ADC not to add its own distortion; the actual signal level buffer is working with is 6Vpp):
These measurements were taken with +/-15V power supply, 2kOhm load, 6Vpp (=0dB) test signal, which was suppressed before the distortion products were measured.
Aleph Bet is a development of the original idea proposed by @Lenin from the RCL-electro.ru forum.
Details will follow shortly.
It uses a composite transistor known as the Baxandall Super Pair (see the attached 1966 article) in the follower role with an Aleph current source (as described in the attached patent by @Nelson Pass) as its load, hence the name. A few twists have been added to that general theme and can be glanced from the simplified schematic:
The distortion performance is quite good (note that this buffer has distortion well below that of the ADC, so the fundamental is suppressed after the buffer and before the ADC in order for the ADC not to add its own distortion; the actual signal level buffer is working with is 6Vpp):
These measurements were taken with +/-15V power supply, 2kOhm load, 6Vpp (=0dB) test signal, which was suppressed before the distortion products were measured.
Aleph Bet is a development of the original idea proposed by @Lenin from the RCL-electro.ru forum.
Details will follow shortly.
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For a device that, ideally, doesn't change the signal in any way, a unity gain buffer is surprisingly useful.
Part of it is impedance matching. Connecting a relatively high impedance output to a relatively low impedance input can potentially overload the source and cause avoidable distortion. A buffer in between would help.
Part of it is frequency dependent impedance. For example, driving a long cable with high capacitance or a transformer's primary by a high impedance source will create non-flat frequency response. A buffer driving that cable or a transformer would be a good idea - see, for example, F6 or M2(x) amplifiers.
But the elephant in the room is the non-linearity of input impedance:
So the key feature of a good buffer is not just making a low impedance into a high impedance. It is the ability to work from a high impedance signal source without adding distortion, plus the ability to provide low impedance drive to whatever cable, transformer or active electronics is connected downstream.
Part of it is impedance matching. Connecting a relatively high impedance output to a relatively low impedance input can potentially overload the source and cause avoidable distortion. A buffer in between would help.
Part of it is frequency dependent impedance. For example, driving a long cable with high capacitance or a transformer's primary by a high impedance source will create non-flat frequency response. A buffer driving that cable or a transformer would be a good idea - see, for example, F6 or M2(x) amplifiers.
But the elephant in the room is the non-linearity of input impedance:
That input capacitance needs to be charged and discharged. Variable capacitance means that the charging current in non-linear. That non-linear current flows through the output impedance of the source. The resulting voltage drop, also non-linear, adds to the signal and manifests as a 20dB/dec THD increase which is very much audible.Bruno Putzeys said:Very few amplifier circuits have a perfectly linear input impedance. It doesn’t even matter whether it’s valves, JFETs or bipolar, op amp or otherwise. All have, to a lesser or greater extent, a variable input capacitance:
Better drive it from a low impedance source such as a good buffer.Bruno Putzeys said:
So the key feature of a good buffer is not just making a low impedance into a high impedance. It is the ability to work from a high impedance signal source without adding distortion, plus the ability to provide low impedance drive to whatever cable, transformer or active electronics is connected downstream.
So many years ago, I kind of fell into buffers when Musical Fidelity was still making the X10 tube buffer. I won't say that it was great, but I will say that it solved some problems with the system that I was using at the time. About that same time a friend of mine was making a passive preamp for me. We tried it out in my system and I could readily hear that it just wasn't sounding full at all. He called it natural sounding until I connected the buffer in between. That woke him up, though he didn't understand the reason at the time.
So, yes, they can be a very useful tool, and yet, if you have lucked with a match that works in your system without one, then consider yourself blessed. Trial and error can be expensive!
So, yes, they can be a very useful tool, and yet, if you have lucked with a match that works in your system without one, then consider yourself blessed. Trial and error can be expensive!
The simplest buffer is an emitter (source, cathode) follower:
Unfortunately, it is not particularly linear. Here is a 2SK170 connected as a follower with a tail resistor, running at Idss=6mA with +/-15V rails. The test signal is 1kHz 6Vpp (2.1V RMS or 6Vpp), and the follower is driving a 47kOhm load with THD=0.028%:
(In this and the following spectra, the 1kHz fundamental with a 0dB (=6Vpp) level is suppressed by ~80dB to eliminate the measurement setup's own distortion.)
The reason for the relatively high distortion is that both the voltage across the JFET and the current through it vary, making the JFET's parameters continuosly change as the signal's momentary value goes up and down.
The standard way to improve linearity is to stabilize the tail current by replacing the resistor with a constant current source, for example, another JFET, as in the First Watt B1:
In this arrangement, an Idss matched pair of 2SK170s gives anorder of magnitude better distortion performance at THD=0.003%, as long as load impedance is high and source impedance is low:
In the post #2 above, I mentioned that a required feature of a buffer is its ability to work from a high impedance signal source without adding distortion. If we increase the source impedance from 1kOhm to, say, 13kOhm - the output impedance of a very reasonable 50k volume control pot at the -6dB position - the distortion performance of the above JFET follower with CCS tail deteriorates to 0.0015%, with higher order harmonics cropping up:
This is rather embarrassing; after all, the buffer is expected to solve the problem of the high output impedance of the source.
That's the result of that variable input capacitance of the top JFET being charged and discharged via the source impedance, with the resulting nonlinear voltage drop adding to the signal. It is possible to significantly reduce this effect by cascoding the top JFET, for example, with another JFET. While we are at it, we can cascode the CCS JFET as well:
Cascoding dramatically reduces both the overall distortion of the follower and the effect of the source impedance. Here is the spectrum at the output of an Idss matched pair (follower+CCS) of 2SK170s, each cascoded by a J113, with 1kOhm source impedance, with THD=37u% (=0.000 037%):
The same buffer with a 13kOhm source gives somewhat more distortion at 75u%, which is still very low:
The remaining limitation is that the load impedance should be high. All the graphs above were taken with the load impedance at 47kOhm. If it is reduced to a very reasonable 10kOhm, the otherwise magnificent cascoded follower with cascoded CCS adds 0.0015% of distortion:
While the THD is still low-ish, it is a disappointing setback from the low distortion with a higher impedance load, particularly for a buffer that is supposed to comfortably drive reasonable loads.
Of course, there is a remedy for that. Stay tuned.
Unfortunately, it is not particularly linear. Here is a 2SK170 connected as a follower with a tail resistor, running at Idss=6mA with +/-15V rails. The test signal is 1kHz 6Vpp (2.1V RMS or 6Vpp), and the follower is driving a 47kOhm load with THD=0.028%:
(In this and the following spectra, the 1kHz fundamental with a 0dB (=6Vpp) level is suppressed by ~80dB to eliminate the measurement setup's own distortion.)
The reason for the relatively high distortion is that both the voltage across the JFET and the current through it vary, making the JFET's parameters continuosly change as the signal's momentary value goes up and down.
The standard way to improve linearity is to stabilize the tail current by replacing the resistor with a constant current source, for example, another JFET, as in the First Watt B1:
In this arrangement, an Idss matched pair of 2SK170s gives anorder of magnitude better distortion performance at THD=0.003%, as long as load impedance is high and source impedance is low:
In the post #2 above, I mentioned that a required feature of a buffer is its ability to work from a high impedance signal source without adding distortion. If we increase the source impedance from 1kOhm to, say, 13kOhm - the output impedance of a very reasonable 50k volume control pot at the -6dB position - the distortion performance of the above JFET follower with CCS tail deteriorates to 0.0015%, with higher order harmonics cropping up:
This is rather embarrassing; after all, the buffer is expected to solve the problem of the high output impedance of the source.
That's the result of that variable input capacitance of the top JFET being charged and discharged via the source impedance, with the resulting nonlinear voltage drop adding to the signal. It is possible to significantly reduce this effect by cascoding the top JFET, for example, with another JFET. While we are at it, we can cascode the CCS JFET as well:
Cascoding dramatically reduces both the overall distortion of the follower and the effect of the source impedance. Here is the spectrum at the output of an Idss matched pair (follower+CCS) of 2SK170s, each cascoded by a J113, with 1kOhm source impedance, with THD=37u% (=0.000 037%):
The same buffer with a 13kOhm source gives somewhat more distortion at 75u%, which is still very low:
The remaining limitation is that the load impedance should be high. All the graphs above were taken with the load impedance at 47kOhm. If it is reduced to a very reasonable 10kOhm, the otherwise magnificent cascoded follower with cascoded CCS adds 0.0015% of distortion:
While the THD is still low-ish, it is a disappointing setback from the low distortion with a higher impedance load, particularly for a buffer that is supposed to comfortably drive reasonable loads.
Of course, there is a remedy for that. Stay tuned.
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Don't mind me, I usually have more to learn than more to say. It just reminded me of the optional transistors that may be used in the N.Pass B1 NuTube preamp. The Sk170 is a substitute for the originals.
But then having said that, my thought was that when a part is chosen for one superior parameter, it brings along with it the downsides. Non the less, as you already have mentioned, it can be dealt with in this case.
But then having said that, my thought was that when a part is chosen for one superior parameter, it brings along with it the downsides. Non the less, as you already have mentioned, it can be dealt with in this case.
Assuming the values noted on the graph are correct,
"tow-order of magnitude better distortion performance at THD=0.0003%,"
Is not it?
Yes, thank you. It should be "two orders of magnitude" then.
On the other hand, that;s kind of low. If you look at Firstwatt B1 manual, it never reaches 0.0003% - although the detailed measurement conditions there are not specified. Perhaps I need to verify than number.
On the other hand, that;s kind of low. If you look at Firstwatt B1 manual, it never reaches 0.0003% - although the detailed measurement conditions there are not specified. Perhaps I need to verify than number.
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I also feel a little too low. 0.000037% for the circuit with cascode bootstrapping also seems too low, but I haven't calculated it yet. The single distortion of the square-law FET is mainly 2nd HD, and the distortion rate tends to increase in proportion to the current change. In the case of a source follower, it takes a feedback of (1+gm*RL), but the tendency does not change. It seems strange that the distortion factor increases by 40 times from 0.000 037% to 0.0015% by changing the load from 47k to 10k.
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I was wrong too. In the case of a source follower, when the load resistance decreases, the current change increases in inverse proportion, and the feedback amount (1+gm*RL) also decreases, so the distortion factor increases in inverse proportion to the square of RL. 47kΩ to 10kΩ is An increase of about 4.7^2=22 times is expected.
Re-measured the simple JFET follower with JFET current source in its tail:
No cascodes, both JFETs are 2SK170 running at Idss (no source resistors). In effect, it is Firstwatt B1, only with higher power supply rails of +/-15V.
The results are similar to the above. Running from 1kOhm source and with 47kOhm load, the distortion is 0.0003% (-110dBc). Raising the source impedance to 13kOhm or lowering the load impedance to 10kOhm increases the distortion by a factor of five, to 0.0016% (-96dBc).
Here are the graphs:
Low source impedance, high load impedance:
Higher source impedance, high load impedance:
Low source impedance, lower load impedance:
Also, here is my measurement rig's own distortion:
and the verification of level calibration by adding a -120dBc signal from a separate generator:
No cascodes, both JFETs are 2SK170 running at Idss (no source resistors). In effect, it is Firstwatt B1, only with higher power supply rails of +/-15V.
The results are similar to the above. Running from 1kOhm source and with 47kOhm load, the distortion is 0.0003% (-110dBc). Raising the source impedance to 13kOhm or lowering the load impedance to 10kOhm increases the distortion by a factor of five, to 0.0016% (-96dBc).
Here are the graphs:
Low source impedance, high load impedance:
Higher source impedance, high load impedance:
Low source impedance, lower load impedance:
Also, here is my measurement rig's own distortion:
and the verification of level calibration by adding a -120dBc signal from a separate generator:
Re-measured the cascoded simple JFET follower with cascoded JFET current source in its tail:
Both cascodes are J113, the follower and CCS JFETs are 2SK170 running at Idss (no source resistors) as above. The pair of 2SK170s is Idss matched, but J113s are unmatched and are different specimens from post #4 above, although from the same bag.
Low source impedance, high load impedance, THD=69u%:
Higher source impedance, high load impedance, THD=96u%:
Low source impedance, lower load impedance, THD=0.0015%
Although the level of distortion in the first two graphs is 5-6dB higher compared to post #4 (mismatched cascodes?), the overall picture is very similar.
Both cascodes are J113, the follower and CCS JFETs are 2SK170 running at Idss (no source resistors) as above. The pair of 2SK170s is Idss matched, but J113s are unmatched and are different specimens from post #4 above, although from the same bag.
Low source impedance, high load impedance, THD=69u%:
Higher source impedance, high load impedance, THD=96u%:
Low source impedance, lower load impedance, THD=0.0015%
Although the level of distortion in the first two graphs is 5-6dB higher compared to post #4 (mismatched cascodes?), the overall picture is very similar.
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As @mason_f8 mentioned above, the increase in distortion with lower load impedance is related to the changing current through the top JFET. By making that current more constant, it is possible to reduce the distortion with low loads.
One approach is the White follower, which senses the current through the top JFET with a small drain resistor and uses the voltage drop across it to modulate the tail current source:
This is a feedback loop, but the loop gain (the value of the sense resistor times the transconductance of the current source JFET) is very low, so it is more about cancellation of one nonlinearity with another than about feedback action. When property tuned, White follower achieves almost perfect cancellation of the second harmonic:
There are two drawback. First, as can be clearly seen in the graph, there is no PSRR. All top rail noise get directly to the gate of the current source and modulates it. Of course, in a single supply scenario we can make the top rail grounded and use a single negative power supply, but it is a workaround and not a solution.
The other problem with the While follower is that its distortion cancellation, unlike proper feedback, depends on many factors (variance in the parameters of FETs, load impedance, supply voltage, temperature, signal amplitude, etc.) and falls apart when any these parameters change. We have seen one example above with 37u% @ 47kOhm load becoming 1500u% @ 10kOhm. The above graph was taken with a 47kOhm load. Plugging in 10kOhm ruins the carefully adjusted cancellation:
It can be adjusted back, but then the performance into 47kOhm would suffer.
A well known fix to the first problem is the Taylor follower:
It adds to the feedback loop a common base PNP (or common gate P-channel) stage, which suppresses the rail noise typically by 40-60dB. Also, it adds a little loop gain but apparently destroys the distortion cancellation. @EUVL offered some stunningly elegant all-JFET implementations of the Taylor follower in his 2008 article on alternative JFET follower configurations.
The current source JFET can be replaced with a BJT or MOSFET:
An obvious variation that I have not seen used is to replace the common base stage with a long-tail pair:
With that current mirror, maybe you don't even need a separate current source anymore:
We walked down this road for a while and obtained some good results, as in better that 0.0001% distortion into a 600ohm load:
(the long line of odd harmonics is from the signal generator, not from the follower).
However, we found more promising an alternative approach of sensing not the current through the top JFET but the output current of the follower. Stay tuned...
One approach is the White follower, which senses the current through the top JFET with a small drain resistor and uses the voltage drop across it to modulate the tail current source:
This is a feedback loop, but the loop gain (the value of the sense resistor times the transconductance of the current source JFET) is very low, so it is more about cancellation of one nonlinearity with another than about feedback action. When property tuned, White follower achieves almost perfect cancellation of the second harmonic:
There are two drawback. First, as can be clearly seen in the graph, there is no PSRR. All top rail noise get directly to the gate of the current source and modulates it. Of course, in a single supply scenario we can make the top rail grounded and use a single negative power supply, but it is a workaround and not a solution.
The other problem with the While follower is that its distortion cancellation, unlike proper feedback, depends on many factors (variance in the parameters of FETs, load impedance, supply voltage, temperature, signal amplitude, etc.) and falls apart when any these parameters change. We have seen one example above with 37u% @ 47kOhm load becoming 1500u% @ 10kOhm. The above graph was taken with a 47kOhm load. Plugging in 10kOhm ruins the carefully adjusted cancellation:
It can be adjusted back, but then the performance into 47kOhm would suffer.
A well known fix to the first problem is the Taylor follower:
It adds to the feedback loop a common base PNP (or common gate P-channel) stage, which suppresses the rail noise typically by 40-60dB. Also, it adds a little loop gain but apparently destroys the distortion cancellation. @EUVL offered some stunningly elegant all-JFET implementations of the Taylor follower in his 2008 article on alternative JFET follower configurations.
The current source JFET can be replaced with a BJT or MOSFET:
An obvious variation that I have not seen used is to replace the common base stage with a long-tail pair:
With that current mirror, maybe you don't even need a separate current source anymore:
We walked down this road for a while and obtained some good results, as in better that 0.0001% distortion into a 600ohm load:
(the long line of odd harmonics is from the signal generator, not from the follower).
However, we found more promising an alternative approach of sensing not the current through the top JFET but the output current of the follower. Stay tuned...
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The Aleph current source was patented in 1998 by Nelson Pass:
The Aleph current source has been used commercially in the Aleph power amplifier series and designed into some of the Zen power amplifiers. It is a modulated current source that appears to be conceived as a drain (collector) load for a common source (common emitter) stage. The current it provides is modulated by the output current of the stage. The Aleph current source senses the output current of the stage with R4 (see the schematic above) and, if the load takes more current, it provides more current; if the load takes less, it provides less. The current through Q1 thus becomes less variable.
As discussed above, the increase in distortion with lower load impedance is related to the changing current through the top JFET. By making that current more constant, it is possible to reduce the distortion with low loads. The Aleph current source surely can help with that! Yet, to the best of my knowledge, the only attempt to use the Aleph current source concept with a source or emitter follower was in the aforementioned article by EUVL. Patrick's implementation used a pair of N-channel and P-channel JFETs instead of a BJT and MOSFET. The follower JFET was not cascoded. That buffer gave a relatively high distortion of 0.045% at 1kHz driving a 1kOhm load to 1V.
I built a cascoded JFET follower as in my posts above, but with an Aleph current source as its load:
The follower is built with a 2SK170GR JFET with Idss=6mA, cascoded by a J113. Since the follower is built with N-channel JFETs, the Aleph current source uses a P-channel FET and an PNP BJT. The BJT's collector load is a monolithic 1mA current source (J505 by Vishay/Siliconix). That current source is critical to the performance of the overall circuit, as it is not enclosed by the Aleph current source's feedback loop; more on this below.
This simple and practical buffer immediately demonstrated some reasonable performance, as in 0.0003% driving a 2kOhm load to 2.1V RMS (about 3V peak):
The distortion performance is limited by the J113 cascode and by the J505 current source. Selecting a different specimen of J113 from the same bag reduced distortion somewhat:
Cascoding the J505 monolithic current source with another J113 reduced the distortion to 60u% (that's 0.000 06%):
Note that even with the cascoded current source, the overall distortion level and the balance between H2 and H3 depends on the follower's cascode, so the J113 may need to be selected for minimal distortion. The difference can be significant, as in 10x (20dB) more H2.
Can we do even better? Yes we can! Stay tuned.
The Aleph current source has been used commercially in the Aleph power amplifier series and designed into some of the Zen power amplifiers. It is a modulated current source that appears to be conceived as a drain (collector) load for a common source (common emitter) stage. The current it provides is modulated by the output current of the stage. The Aleph current source senses the output current of the stage with R4 (see the schematic above) and, if the load takes more current, it provides more current; if the load takes less, it provides less. The current through Q1 thus becomes less variable.
As discussed above, the increase in distortion with lower load impedance is related to the changing current through the top JFET. By making that current more constant, it is possible to reduce the distortion with low loads. The Aleph current source surely can help with that! Yet, to the best of my knowledge, the only attempt to use the Aleph current source concept with a source or emitter follower was in the aforementioned article by EUVL. Patrick's implementation used a pair of N-channel and P-channel JFETs instead of a BJT and MOSFET. The follower JFET was not cascoded. That buffer gave a relatively high distortion of 0.045% at 1kHz driving a 1kOhm load to 1V.
I built a cascoded JFET follower as in my posts above, but with an Aleph current source as its load:
The follower is built with a 2SK170GR JFET with Idss=6mA, cascoded by a J113. Since the follower is built with N-channel JFETs, the Aleph current source uses a P-channel FET and an PNP BJT. The BJT's collector load is a monolithic 1mA current source (J505 by Vishay/Siliconix). That current source is critical to the performance of the overall circuit, as it is not enclosed by the Aleph current source's feedback loop; more on this below.
This simple and practical buffer immediately demonstrated some reasonable performance, as in 0.0003% driving a 2kOhm load to 2.1V RMS (about 3V peak):
The distortion performance is limited by the J113 cascode and by the J505 current source. Selecting a different specimen of J113 from the same bag reduced distortion somewhat:
Cascoding the J505 monolithic current source with another J113 reduced the distortion to 60u% (that's 0.000 06%):
Note that even with the cascoded current source, the overall distortion level and the balance between H2 and H3 depends on the follower's cascode, so the J113 may need to be selected for minimal distortion. The difference can be significant, as in 10x (20dB) more H2.
Can we do even better? Yes we can! Stay tuned.
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Hi ! very interesting thread indeed Could share more details about the circuit responsible for this HD spectrum ?
https://www.diyaudio.com/community/.../1102236-8026dfa99f5345fed3e6eb07b55a0b18.jpg
it looks impressive
The other spectra are good but the fundamental is very low level Almost all buffers behave very well with small V input signal
The challenge is to find one good also with some Volts input signals The performance degrades very evidently
https://www.diyaudio.com/community/.../1102236-8026dfa99f5345fed3e6eb07b55a0b18.jpg
it looks impressive
The other spectra are good but the fundamental is very low level Almost all buffers behave very well with small V input signal
The challenge is to find one good also with some Volts input signals The performance degrades very evidently
This buffer has distortion well below that of the ADC, so for measurements, the fundamental is suppressed after the buffer-under-test and before the ADC in order for the ADC not to add its own distortion. The actual signal level buffer is handling is annotated on each chart, e.g. "2.1V RMS" in the post #15 above.
The circuit responsible for the last spectrum in the post #14 is shown, in its simplified form, just above that chart. Not shown are the frequency compensation and the values, plus a couple of other details.
I plan to resurrect this thread later this year and show additional details.
The circuit responsible for the last spectrum in the post #14 is shown, in its simplified form, just above that chart. Not shown are the frequency compensation and the values, plus a couple of other details.
I plan to resurrect this thread later this year and show additional details.
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Hi do you mean this one ? https://www.diyaudio.com/community/attachments/k170-j113-aleph-sch-png.1206117/
Low at such level that going lower will not provide a perceptible improvement when listening in a rather revealing system
i do not know how translate this in dB -100dB 2nd harmonic and the other harmonics lower ?
i am attaching an attempt of sim I have replaced the the J505 current source with a resistor because i could not find it in the library
I am using the current version of LTSPice downloaded from here
https://www.analog.com/en/resources/design-tools-and-calculators/ltspice-simulator.html
Low at such level that going lower will not provide a perceptible improvement when listening in a rather revealing system
i do not know how translate this in dB -100dB 2nd harmonic and the other harmonics lower ?
i am attaching an attempt of sim I have replaced the the J505 current source with a resistor because i could not find it in the library
I am using the current version of LTSPice downloaded from here
https://www.analog.com/en/resources/design-tools-and-calculators/ltspice-simulator.html
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