Done. Assuming Rbb=0 (which may not be true) the maximum SNR is exactly where gm*Rs=1 so (surprise, surprise) Richard was exactly right, the maximum SNR is where Rs=1/gm. Otherwise said, the maximum power transfer condition coincides exactly with the maximum SNR condition. That's very specific to the common base stage, no generalization possible as far as I can tell.
I've built a spreadsheet, the maximum is very flat though, no fine optimization is required. For a 12ohm MC cartridge I get the maximum SNR anywhere between 1mA and 3mA, SNR variation across is about 0.5dB.
I'll do the same, considering Rbb this time. Rbb noise is fully amplified by the gain stage, no input divider like for the Rs noise.
Once again, all this holds for the sigle transistor common base, no complementary stuff yet.
@Bill,
For me you are the Wiki when it comes to Cart Specifications.
I have this question:
Is it safe to assume that output voltages for MC Carts are given with the recommended termination in place (mostly somewhere like 10*Rcart) ?
If not, output voltage would be attenuated by this termination.
I need this info when adding a termination resistor to the formula in #541, that's why.
Hans
For me you are the Wiki when it comes to Cart Specifications.
I have this question:
Is it safe to assume that output voltages for MC Carts are given with the recommended termination in place (mostly somewhere like 10*Rcart) ?
If not, output voltage would be attenuated by this termination.
I need this info when adding a termination resistor to the formula in #541, that's why.
Hans
Here's the test report of a virt. gnd MC Amp that I was looking for.
B.M.C. Phono MCCI phono preamplifier | Stereophile.com
Funny enough, to measure S/N they short circuited the input and came to a figure of 99.9 and 103.3 dB-A resp for the L/R channel !
But apart from that, they were extremely charmed by the sound of this topology.
Hans
Is this feedback derived or open-loop virtual ground, another topology with different behavior.
They talk about Current Input, so it seems safe to assume that it it is feedback derived.
Hans
I just went through the sterophile test report referenced by Hans.
The BMC input stage is claimed to be a balanced input with a current to voltage converter as a first stage with a 3 Ohm input impedance. Furthermore it is claimed that this input stage is based on a BJT common base architecture with 5 or 10 transistors in parrallel (its not clear if the mentioned 10 transistors are for one polarity of the balanced signal input only or for both). It is also stated that the input stage is feedback free.
The measurement section describes an unweighted signal to noise ratio to be in the lower 70 dBs range. When A-weighted the ratio improves by more than 30 dB! to 103 dB-A for the right channel.
The shown distortion measurement (on a linear frequency scale) shows a massive increase in noise level towards frequencies below a few hundered Hz.
The BMC input stage is claimed to be a balanced input with a current to voltage converter as a first stage with a 3 Ohm input impedance. Furthermore it is claimed that this input stage is based on a BJT common base architecture with 5 or 10 transistors in parrallel (its not clear if the mentioned 10 transistors are for one polarity of the balanced signal input only or for both). It is also stated that the input stage is feedback free.
The measurement section describes an unweighted signal to noise ratio to be in the lower 70 dBs range. When A-weighted the ratio improves by more than 30 dB! to 103 dB-A for the right channel.
The shown distortion measurement (on a linear frequency scale) shows a massive increase in noise level towards frequencies below a few hundered Hz.
When you short cut the virtual gnd input of an Amp, it will multiply its offset voltage with its open loop gain.
In other words, its output will clip either positive or negative.
So this measurement is plain nonsense.
I communicated that with JA and he admitted that this was wrong.
Hans
Whew, this was rather ugly. No closed for solution, since the SNR optimum is the root of a 3rd degree polynomial. Here's a couple of examples to see the Rbb effect on the optimum Ic
Rs=12ohm
Vs=0.4mV
Rbb=0ohm
------------
Ic=1.2mA
Rs=12ohm
Vs=0.4mV
Rbb=2ohm
------------
Ic=1mA
Rs=12ohm
Vs=0.4mV
Rbb=4ohm
------------
Ic=0.9mA
SNR varies with 1.6dB
Rs=5ohm
Vs=0.4mV
Rbb=0ohm
------------
Ic=2.9mA
Rs=5ohm
Vs=0.4mV
Rbb=2ohm
------------
Ic=2.2mA
Rs=5ohm
Vs=0.4mV
Rbb=4ohm
------------
Ic=1.8mA
SNR varies with 3.2dB
So for MC cartridges with very low impedance (here, 5ohm) the SNR optimum is relevant and of course Rbb has a significant effect.
For MC cartridges with higher impedance (12ohm, this is my current Benz Micro Gold low output) the optimum is rather flat and (as expected) the Rbb doesn't matter much.
Very happy I got a new tool to optimize the bias of these common base virtual ground head amps
.
Syn08, just out of curiousity, putting your 6 examples in my formula in #541 and subtracting 7.9dB to convert it to flat noise without weighting, gives resp the following results when using RTI=Sqrt[(Rbb+1/gm)/60]:
71.7 dB
71.0 dB
70.5 dB, delta in SNR is 1.2 dB
75.6 dB
74.3 dB
73.3 dB, delta in SNR is 2.3dB
To get some better insight, maybe you could comment on how far these 6 figures deviate from your more accurate SNR calculations.
Hans
71.7 dB
71.0 dB
70.5 dB, delta in SNR is 1.2 dB
75.6 dB
74.3 dB
73.3 dB, delta in SNR is 2.3dB
To get some better insight, maybe you could comment on how far these 6 figures deviate from your more accurate SNR calculations.
Hans
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Very happy I got a new tool to optimize the bias of these common base virtual ground head amps
Single ended? Do you have a basic schematic?
This was exactely my first thought as well. If it is a virtual ground input realized with an OPAMP you are absolutely right.
But the high level circuit description says that the the input stage is not an OPAMP and that there is no negative feedback loop to create a virtual ground.
This was exactely my first thought as well. If it is a virtual ground input realized with an OPAMP you are absolutely right.
But the high level circuit description says that the the input stage is not an OPAMP and that there is no negative feedback loop to create a virtual ground.
The manufacturers factsheet tells that there is global feedback, so read Stereophiles report with suspicion.
Hans
Very large differences in SNR, and that's to be expected. The input signal and the Rs noise are divided by the voltage divider of Rs and the (low) input impedance of the common base. At the same time, the noise is not, so the SNR in my case is much lower (up to 30dB lower), and this is to be expected. This divider is why I said this optimum exists only for the very low input impedance of the common base (essentially 1/gm).
I've mentioned a few posts up why a gm optimum exists.
For the easy no Rbb case
Psig=G^2*Vs^2/(1+gm*Rs)^2
Pnoise=G^2*4KT*Rs*(1+2*gm*Rs)/[2*gm*Rs*(1+gm*Rs)]
you do the ratio (the gain G goes away and separate the constant factor Vs^2/(4kT*Rs)) calculate the derivative of the expression (as a function of gm*Rs), make it 0 and calculate the optimum gm*Rs. Plug it back in the SNR and you'll get the optimum SNR for that gm*Rs. Then calculate the optimum Ic, given Gm and Rs.
Attached is a plot of SNR[dB] vs. Ic[mA] for Rs=12ohm Vs=0.4mV and Rbb=0. Note the Ic horizontal log scale. The optimum Ic goes down when Rbb is considered.
Attachments
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Off the top of my head I don't know and will have to go and look around for an answer. I had always assumed it was with the recommended load, but the more I look at cart specs the more I realise some of them are plucked out of thin air!