Have been playing with this circuit
from Merlin's page here The Valve Wizard
I can't figure out how to calculate the frequency response effect of the bootstrap cap. Any ideas? I'm using a variety of tubes and resistors. So am curious about this.
(pic reproduced without permission, but with much respect)
from Merlin's page here The Valve Wizard
I can't figure out how to calculate the frequency response effect of the bootstrap cap. Any ideas? I'm using a variety of tubes and resistors. So am curious about this.
(pic reproduced without permission, but with much respect)
It will probably add an LF shelf. Estimating the size of the shelf is fairly easy. Calculating it accurately is a bit more complicated.
To estimate:
At high frequencies when the bootstrap is effective you can assume the amplifier valve sees an infinite anode load, so gain is mu (assuming cathode is decoupled).
At low frequencies when the bootstrap is ineffective you can assume the anode sees the two resistors in series, so gain is mu x (R1+R2)/(Ra+R1+R2) where Ra is anode impedance (Rp for Americans).
So the size of the shelf is (R1+R2)/(Ra+R1+R2).
This estimate assumes the CF is ideal and/or unloaded. Neither assumption is true, but both are near enough true for many practical purposes. One thing to watch is that when a bootstrap is used it raises the output impedance of the CF by a ratio approximately given by (Ra+R2)/Ra.
The frequency where this shelf occurs will roughly be given by f = 1/( 2pi C1 R1 ).
To estimate:
At high frequencies when the bootstrap is effective you can assume the amplifier valve sees an infinite anode load, so gain is mu (assuming cathode is decoupled).
At low frequencies when the bootstrap is ineffective you can assume the anode sees the two resistors in series, so gain is mu x (R1+R2)/(Ra+R1+R2) where Ra is anode impedance (Rp for Americans).
So the size of the shelf is (R1+R2)/(Ra+R1+R2).
This estimate assumes the CF is ideal and/or unloaded. Neither assumption is true, but both are near enough true for many practical purposes. One thing to watch is that when a bootstrap is used it raises the output impedance of the CF by a ratio approximately given by (Ra+R2)/Ra.
The frequency where this shelf occurs will roughly be given by f = 1/( 2pi C1 R1 ).
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Thanks. Since posting I did some simulation, and confirmed the shelf response.
One thing: As above f the load is effectively infinite, we have constant current, so isn't a cathode decoupling cap unnecessary? Because I was using no cap and low Ra valves with fairly high R1 and R2, I think this was the main gain advantage I was getting.
Edit: I just tested it with and without a coupling cap, there is some difference, but not much, and my bootstrap shelf was occurring at 70Hz, so below guitar frequencies.
In general though, the bootstrap seems to just sound good, even if I factor in the gain change by upping the input signal. Bootstrap mojo, I guess. Or maybe that worsening of impedance.
One thing: As above f the load is effectively infinite, we have constant current, so isn't a cathode decoupling cap unnecessary? Because I was using no cap and low Ra valves with fairly high R1 and R2, I think this was the main gain advantage I was getting.
Edit: I just tested it with and without a coupling cap, there is some difference, but not much, and my bootstrap shelf was occurring at 70Hz, so below guitar frequencies.
In general though, the bootstrap seems to just sound good, even if I factor in the gain change by upping the input signal. Bootstrap mojo, I guess. Or maybe that worsening of impedance.
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With an infinite load you don't need a cathode decoupling cap, but then you can only apply an infinite load. A real CF is not an infinite load. Of course, at really low frequencies you lose both the decoupling and the bootstrapping so you can get two LF shelves which may or may not overlap.
The bootstrap seems to have a good reputation among people who have tried it. It is a close relative of the SRPP. Other things being equal the SRPP may be better, but the bootstrap circuit has the advantage that the CF part can be run at higher current for better driving capability.
The bootstrap seems to have a good reputation among people who have tried it. It is a close relative of the SRPP. Other things being equal the SRPP may be better, but the bootstrap circuit has the advantage that the CF part can be run at higher current for better driving capability.
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