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♦ i ♦ ♦ ii ♦ Improving the Cascode's PSRR High Transconductance In the Grounded Cathode amplifier the transconductance of the triode is mitigated by the addition of the plate resistor. Ra Review of the Cascode's Operation when summed with the plate resistance and divided into the The Cascode is a compound amplifier. One triode stands on mu of the triode, yields the resulting transconductance: top of another, while sharing a common current path. The top Gm = mu / (rp + Ra). triode strives both to shield the input grid from the top This decrease in transconductance reduces the potential triode's Miller effect and to preserve the transconductance of gain of the amplifier. In the Cascode amplifier, on the other the bottom triode. The result is amplifier with both high gain hand, the bottom triode's transconductance is nearly identical and extended bandwidth. 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 Cascode & Grounded Cathode Amplifiers capacitance greatly reduces the high frequency response of the amplifier; whereas in the Cascode amplifier, the input Cascode VS Grounded Cathode grid-to-plate capacitance is virtually identical to its static So far, in terms of transconductance and low input value, as its plate voltage is held at a nearly constant value. 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. Textbook Grounded Cathode Amplifier The Grounded Cathode amplifier achieves a respectable PSRR figure, as the rp of the triode defines the bottom the bottom triode's rp. The gain from the second input: element of a voltage divider, with the plate resistor defining Gain = mu Ra / [ Ra + (mu + 1) Rk ]. the top element: For example, using a 6DJ8 with a plate resistor of 10K, the Ratio = rp / (rp + Ra). gain equals: On the other hand, the Cascode's high output impedance Gain = mu Ra / [ Ra + (mu + 1) rp ] makes for a poor noise division: Gain = 33 10,000 / [ 10,000 + (33 + 1) 3,000 ] Ratio = (mu + 2) rp / [(mu + 2) rp + Ra]. Gain = 330,000 / [ 10,000 + 102,000 ] For example, a 6DJ8 used in a Grounded Cathode amplifier Gain = 2.94. with a 9K plate load resistor and a bypassed cathode resistor, Now this gain from the second input can be used to will allow only 25% of the noise at its power supply interject a sampling of the power supply noise, which will be connection to make to its output, as its 3K rp defines only in inverted phase at the output. If this inverted noise signal is one quarter of the resistance presented to the power supply to equal in amplitude to the power supply noise, the two will ground: null at the output. From the example above, the needed ratio Ratio = rp / (rp + Ra) of power supply noise is 1/2.94. Ratio = 3,000 / (3000 + 9,000) Ratio = 3,000 / 12,000 A Tweak Ratio = 1 / 4 = .25. Now as tubes differ from each other and even differ from When the 6DJ8 is used in a Cascode circuit, with the same themselves over time, the best solution is not to hard-wire 9K plate resistor, allows 92% of the noise at its power supply the ratio in place, but to use a potentiometer to allow a fine connection to make to its output; the math: degree of noise nulling. The nulling can be adjusted for a Ratio = (mu + 2) rp / [(mu + 2) rp + Ra] signal stage or if the Cascode appears in a more complex Ratio = (33 +2) 3,000 / [(mu + 2) 3000 + 9,000] circuit, to null the noise at the final output, as long as the Ratio = 105,000 / 114,000 phase shift between stages is nominal and the gain from the Ratio = 1 / 1.086 = 0.92. second input is sufficient to overwhelm the noise added from the other stages.

A Further Tweak The Solution to a Poor PSRR The Cascode circuit, when using triodes, has actually two Placing the potentiometer between inputs available. The first is the bottom triode's grid; the two resistors will allow more range of second, the top triode's grid. Normally, this second input is noise nulling, as at one extreme, in the used only to connect to a fixed reference voltage, but it can example at the left, the maximum noise also be used as a low-gain signal input. This is possible interjection is 50%: because of the triode's plate resistance. The rp of the bottom Ratio = 20K / (20K + 10K + 10K) triode allows the bottom triode to function like the Ratio = 20K / 40K unbypassed cathode resistor in a Grounded Cathode Ratio = .5 amplifier. In other words, the top triode functions as a and at the other extreme, the noise Grounded Cathode amplifier with its cathode in series with 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