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Improving the Cascode's PSRR
Review of the Cascode's Operation
The Cascode is a compound amplifier. One triode stands on
top of another, while sharing a common current path. The top
triode strives both to shield the input grid from the top
triode's Miller effect and to preserve the transconductance of
the bottom triode. The result is amplifier with both high gain
and extended bandwidth.
High Transconductance
In the Grounded Cathode amplifier the transconductance of
the triode is mitigated by the addition of the plate resistor. Ra
when summed with the plate resistance and divided into the
mu of the triode, yields the resulting transconductance:
Gm = mu / (rp + Ra).
This decrease in transconductance reduces the potential
gain of the amplifier. In the Cascode amplifier, on the other
hand, the bottom triode's transconductance is nearly identical
to its static value. The resistance R presented at its plate is
equal to the top triode's rp added to the plate resistor's value
divided by its mu:
R = (rp + Ra) / mu.
The result of this resistance R in parallel with the rp of the
bottom triode divided into the mu of the triode yields the
resulting transconductance:
Gm = mu / (rp + R).
Textbook Cascode Amplifier
Low Input Capacitance
In the Grounded Cathode amplifier, the grid-to-plate
capacitance is multiplied by the gain that the triode realizes
working into its plate resistor. This effective increase in
capacitance greatly reduces the high frequency response of
the amplifier; whereas in the Cascode amplifier, the input
grid-to-plate capacitance is virtually identical to its static
value, as its plate voltage is held at a nearly constant value.
Textbook Grounded Cathode Amplifier
Cascode & Grounded Cathode Amplifiers
Cascode VS Grounded Cathode
So far, in terms of transconductance and low input
capacitance, the Cascode seems like a clear winner. Where it
falls short is in its high output impedance and a near zero
PSRR. With the Grounded Cathode amplifier, the output
impedance is equal to Ra || rp; with the Cascode, the output
impedance is equal to Ra || (mu + 2) rp. For example, a
6DJ8 used in a Grounded Cathode amplifier with a 9K plate
load resistor and a bypassed cathode resistor, will have a Zo
at its output of 2,250 ohms:
Zo = Ra || rp
Zo = 9,000 || 3,000
Zo = 2,250
When the 6DJ8 is used in a Cascode circuit, with the same
9K plate resistor, the math look like this:
Zo = Ra || (mu + 2) rp
Zo = 9,000 || (33 + 2) 3,000
Zo = 8,270.
The Grounded Cathode amplifier achieves a respectable
PSRR figure, as the rp of the triode defines the bottom
element of a voltage divider, with the plate resistor defining
the top element:
Ratio = rp / (rp + Ra).
On the other hand, the Cascode's high output impedance
makes for a poor noise division:
Ratio = (mu + 2) rp / [(mu + 2) rp + Ra].
For example, a 6DJ8 used in a Grounded Cathode amplifier
with a 9K plate load resistor and a bypassed cathode resistor,
will allow only 25% of the noise at its power supply
connection to make to its output, as its 3K rp defines only
one quarter of the resistance presented to the power supply to
ground:
Ratio = rp / (rp + Ra)
Ratio = 3,000 / (3000 + 9,000)
Ratio = 3,000 / 12,000
Ratio = 1 / 4 = .25. When the 6DJ8 is used in a Cascode circuit, with the same
9K plate resistor, allows 92% of the noise at its power supply
connection to make to its output; the math:
Ratio = (mu + 2) rp / [(mu + 2) rp + Ra]
Ratio = (33 +2) 3,000 / [(mu + 2) 3000 + 9,000]
Ratio = 105,000 / 114,000
Ratio = 1 / 1.086 = 0.92. The Solution to a Poor PSRR
The Cascode circuit, when using triodes, has actually two
inputs available. The first is the bottom triode's grid; the
second, the top triode's grid. Normally, this second input is
used only to connect to a fixed reference voltage, but it can
also be used as a low-gain signal input. This is possible
because of the triode's plate resistance. The rp of the bottom
triode allows the bottom triode to function like the
unbypassed cathode resistor in a Grounded Cathode
amplifier. In other words, the top triode functions as a Grounded Cathode amplifier with its cathode in series with
the bottom triode's rp. The gain from the second input:
Gain = mu Ra / [ Ra + (mu + 1) Rk ]. For example, using a 6DJ8 with a plate resistor of 10K, the
gain equals:
Gain = mu Ra / [ Ra + (mu + 1) rp ]
Gain = 33 10,000 / [ 10,000 + (33 + 1) 3,000 ]
Gain = 330,000 / [ 10,000 + 102,000 ]
Gain = 2.94.
Now this gain from the second input can be used to
interject a sampling of the power supply noise, which will be
in inverted phase at the output. If this inverted noise signal is
equal in amplitude to the power supply noise, the two will
null at the output. From the example above, the needed ratio
of power supply noise is 1/2.94.
A Tweak Now as tubes differ from each other and even differ from
themselves over time, the best solution is not to hard-wire
the ratio in place, but to use a potentiometer to allow a fine
degree of noise nulling. The nulling can be adjusted for a
signal stage or if the Cascode appears in a more complex
circuit, to null the noise at the final output, as long as the
phase shift between stages is nominal and the gain from the
second input is sufficient to overwhelm the noise added from
the other stages.
A Further Tweak
Placing the potentiometer between
two resistors will allow more range of
noise nulling, as at one extreme, in the
example at the left, the maximum noise
interjection is 50%:
Ratio = 20K / (20K + 10K + 10K)
Ratio = 20K / 40K
Ratio = .5
and at the other extreme, the noise
interjection is 25%:
Ratio = 10K / (20K + 10K + 10K)
Ratio = 10K / 40K
Ratio = .25.
At the middle position of the
potentiometer, the noise interjection is 37.5%:
Ratio = (10K + 5K) / (20K + 10K + 10K)
Ratio = 15K / 40K
Ratio = .375. // John Broskie 1999