Bob Cordell said:
Yes, it is very nice work.
It gives an explanation for my failure to see this phenomenon in
degenerated JFETs down to .001%. The higher order harmonics
appear to go down as the square of the open loop distortion figure.
I'll just have to drive those poor little JFETs harder...
😎
Thanks Nelson. If it helps clear up the mystery with the degeneration, that makes me happy.
I believe the way it works with the harmonic numbers is as follows (per this post)
Dropping the open-loop fractional second harmonic distortion by x dB is equivalent to dropping the input signal by x db. This would in turn have the following effects:
1) Closed-loop fractional second harmonic would also drop by x dB
2) Closed-loop fractional third harmonic would drop by 2x dB (as the square of the open-loop fractional second harmonic, per your observation).
3) Closed-loop fractional fourth harmonic would drop by 3x dB (as the cube of the open-loop fractional second harmonic).
4) Closed-loop fractional fifth harmonic would drop by 4x dB (as the fourth power of the open-loop fractional second harmonic).
...etc etc for higher closed-loop harmonics. "Fractional" in this context refers to the ratio of the harmonic to the fundamental.
Let me know if you disagree and if so why.
I believe the way it works with the harmonic numbers is as follows (per this post)
Dropping the open-loop fractional second harmonic distortion by x dB is equivalent to dropping the input signal by x db. This would in turn have the following effects:
1) Closed-loop fractional second harmonic would also drop by x dB
2) Closed-loop fractional third harmonic would drop by 2x dB (as the square of the open-loop fractional second harmonic, per your observation).
3) Closed-loop fractional fourth harmonic would drop by 3x dB (as the cube of the open-loop fractional second harmonic).
4) Closed-loop fractional fifth harmonic would drop by 4x dB (as the fourth power of the open-loop fractional second harmonic).
...etc etc for higher closed-loop harmonics. "Fractional" in this context refers to the ratio of the harmonic to the fundamental.
Let me know if you disagree and if so why.
andy_c said:
Yes, the third order intercept concept from RF. Like diff-gain/phase not exactly unknown. BIG->🙂
scott wurcer said:
Yes!
I used to work on radar receivers in the defense business for many years, and you could see these relationships on a spectrum analyzer (which we did with odd-order intermods rather than harmonics).
andy_c said:
If you want to carry it further I bet the conformance of some simple op-amp/feedback circuits to this relationship (from very small signal and up) ties into the whole TIM thing. The idea is quantifying the level at which small signal behavior transitions into large signal behavior. Quite a few lost lunch hours arguing over this.
Do you mean something like this?
Soft TIM -> weakly nonlinear
Hard TIM -> strongly nonlinear (the dB multiples relationship for each harmonic or intermod breaks down)
Soft TIM -> weakly nonlinear
Hard TIM -> strongly nonlinear (the dB multiples relationship for each harmonic or intermod breaks down)
Something important to remember is that you have to either isolate
or factor in the distortion associated with variations in Vds (or Vce)
when you are looking at these phenomena.
I used cascoding to freeze Vds in my results, but in my previously
posted circuit with the harmonics of the power Mosfet, the Vds
variations are large, creating lots of higher order content even without
degeneration. With cascoding or dramatic reduction of the 8 ohm load
on that circuit, I would expect it to fall more in line with Andy's results.
😎
or factor in the distortion associated with variations in Vds (or Vce)
when you are looking at these phenomena.
I used cascoding to freeze Vds in my results, but in my previously
posted circuit with the harmonics of the power Mosfet, the Vds
variations are large, creating lots of higher order content even without
degeneration. With cascoding or dramatic reduction of the 8 ohm load
on that circuit, I would expect it to fall more in line with Andy's results.
😎
Yes, not a hard and fast rule but a way to quantify amplifiers. An interesting possible study let's say. Maybe gain of ten followers, first few harmonics plotted vs output level and see if there is any correllation with anything else.
Nelson Pass said:
This came up in the Blowtorch thread a while back too. PMA was doing some simulations of a circuit similar to John's and was surprised that third and higher harmonics were showing up. By setting the LAMBDA parameter in the FET model to zero (taking away the variation of Id with Vds), those higher-order products went away. My memory of this is foggy, but I believe he cascoded the circuit and got rid of the higher-order stuff in the sim even with LAMBDA not zero.
Of course, my recent sims here are idealized to an unrealistic extent. But as mentioned, their purpose was to look at theoretical behavior.
And as Scott has pointed out, the ancient JFET SPICE model is very inaccurate at predicting distortion.
andy_c said:
I recall bugging PMA to cascode the JFETs in his sims. 🙂
I get just about your number for 3rd harmonic with 12 dB of
degeneration on a cascoded JFET which has a 1% open loop 2nd
harmonic. Higher orders and figures for lesser open loop distortions
are in the dirt on my AP1 coupled to a pc based spectrum analyzer.
😎
Great! Good to get some experimental verification. I'd expect my numbers to be optimistic compared to the real world.
Wait, wait. The number of equations will be doubled (two devices), thus more high-order staff will be in the output signal.
Clearly you will never get perfection on this. There will always be
a finite impedances on all three pins of the device, and you will
never truly lock the Vds to a constant.
In real life, cascoding is probably the best approach if you still want
the part to actually do something useful.
😎
a finite impedances on all three pins of the device, and you will
never truly lock the Vds to a constant.
In real life, cascoding is probably the best approach if you still want
the part to actually do something useful.
😎
I thought I remembered you saying once before that Cascoding does not always bring improvements ?
So when not to use cascode ?
Patrick
So when not to use cascode ?
Patrick
Cascoding does change the sound, and depending on your taste, it's
not always for the better, particularly in output stages.
Also, there are times when you want to work the load line for lower
distortion, letting the gain variations due to Vds cancel the 2nd
harmonic due to current. A fine example is with JFET followers,
where you can get the distortion down to about .0007% into 10 Kohm
at a volt. What remains, of course is mostly 3rd harmonic.
And of course you can cascode so as to deliberately set up a specific
load line, such as with the F3, which gets as low as .002% at 1 watt,
allowing specific Vds variation with current.
😎
not always for the better, particularly in output stages.
Also, there are times when you want to work the load line for lower
distortion, letting the gain variations due to Vds cancel the 2nd
harmonic due to current. A fine example is with JFET followers,
where you can get the distortion down to about .0007% into 10 Kohm
at a volt. What remains, of course is mostly 3rd harmonic.
And of course you can cascode so as to deliberately set up a specific
load line, such as with the F3, which gets as low as .002% at 1 watt,
allowing specific Vds variation with current.
😎
Or minimize variations of both currents and voltages, like bootstrapped at drain source follower loaded on counter-modulated CCS. I got nice results such a way: in line out buffers, in headphone amps, in output tube grids' drivers, and in class A stage of class A+C amps. When such amps are also surrounded by a common FB loop they sound as if all tubey, no audible errors.
> Also, there are times when you want to work the load line for lower distortion, letting the gain variations due to Vds cancel the 2nd harmonic due to current.
Isn't it not much better to cancel even harmonics using balanced circuits, and only optimise the load line to minimise 3rd and 5th ?
How could cascoding be employed to benefit in that sense ?
Would you perhaps be kind enough to post an example ?
Thx,
Patrick
Isn't it not much better to cancel even harmonics using balanced circuits, and only optimise the load line to minimise 3rd and 5th ?
How could cascoding be employed to benefit in that sense ?
Would you perhaps be kind enough to post an example ?
Thx,
Patrick
Wavebourn,
In the first place, it is not easy to make useful measurements with the current ancient, lousy standards. Proposals for redefinition, aiming better agreement with the perceived sound, will unlikely be embraced by the industry. Why complicate things? The present standards serve their purpose (to convince buyers) well.
Harmonic multiplication occurs in that way all right, although a more balanced picture in this and other respect can be given, showing fundamental differences between local feedback and feedback through multiple stages.