Feedback Stability FAQ Project
Prior to creating a feedback amplifier and stabilizing it,
a conventional amplifier is presented. This example creates
a 2 stage 6SN7GTA/B amplifier, analyzes it for gain, finds the
poles and zeros of the amplifier, and presents the frequency
response from the analyzed amplifier.
BOUNDARY CONDITIONS:
2 Stage 6SN7GTA or GTB amplifier.
Filament: 6.3V AC or DC, 600 mA.
High Tension: 400 volts DC. Regulated and filtered.
Input: 1 volt RMS behind a source resistance of 10k.
Output Load: 31.6k and 100pF load capacitance.
Standard 1 or 5% valued components utilized.
The Circuit:
0.15 uF to first stage grid, 210k resistor grid to ground.
First stage cathode: Unbypassed cathode resistor of 887 ohms.
First stage plate (anode): 22k resistor to high voltage supply.
First stage plate to second stage grid: 0.22 uf.
Second stage grid 71.5k resistor to ground.
Second stage cathode: 715 ohms paralleled with 68 uF cap to gnd.
Second stage plate: 12k resistor to high voltage supply, 1 uF
to the output.
DC Conditions:
The first stage is biased at 7 volts on the cathode and runs
at 8 mA. The Plate voltage is 225 volts. Under these conditions,
the 6SN7 has a plate resistance of 8000 ohms (neglecting the
cathode degeneration temporarily), and a transconductance of 2.5 mS.
The second stage is biased at 8 volts on the cathode and about
11.3 mA. The plate voltage is 265 volts. Under these conditions,
the 6SN7 has a plate resistance of 7200 ohms and a transconductance
of 2.8 mS. (Thats 2800 umhos to some of us.) Notice the second
stage tube is dissipating slightly less than 3 watts, no problem.
Midband Gain:
There is about 0.5 dB loss from the voltage division of the 10k
source resistance and the 210k grid resistor.
The first stage gain is about 4.2, or 12.5 dB. (The way to get this
is to take the TOTAL plate circuit resistance divided by the total
cathode circuit resistance... 8k paralleled with 22k paralleled
with 71.5k (5.42k) divided by 887+400 (1/gm)).
The second stage gain is about 11, or 21 dB. (12k paralleled with
7.2k paralleled with 31.6k (3.94k) divided by 357 (1/gm)).
Thus, the overall midband gain is about 44, or 33 dB.
Low Frequency Poles and Zeros:
The input coupling capacitor forms a pole at 5 Hz. (1/2*pi*r*c).
There is a zero at DC. The coupling from the first to the second
stage forms a pole at 10 Hz. There is another zero at DC.
The coupling to the output forms another pole at 5 Hz. There is
a zero at DC. The cathode bypass on the second stage forms a pole-
zero pair. The zero is at 1.66 Hz, and the pole is at 5 Hz. This is
a little trickier to figure, and can best be visualized as follows:
As you DECREASE frequency, the capacitor begins to look like an
open circuit, causing gain to decrease as you LOWER frequency. This
is the pole position. At some yet lower frequency, the capacitor is
invisible and some lower gain is produced. This is the zero.
The pole is at f = 1/(2*pi*c*(Rk paralleled with (1/gm))). The
zero is at f = 1/(2*pi*c*Rk).
Summary: 3 zeros at DC, a zero at 1.66 Hz, 3 poles at 5 Hz, 1 pole
at 10 Hz.
High Frequency Poles:
Due to the finite source resistance, there is a high frequency
pole at the circuit input. This is 10k and the input capacitance
of the first stage and any wiring capacitance. With a gain of 4.2,
the 4 pF Cgp is multiplied to 17 pF, added to 2 pF Cgk and about
5 pF wiring capacitance or a total of 24 pF. With a 10k source,
this produces a pole at 600 kHz. Due to the cathode degeneration,
the effective plate resistance will be multiplied by the gain
reduction due to degeneration, or about 25k. The high frequency
resistance is therefore 22k paralleled with 25k paralleled with
71.5k, or about 10.2k. The capacitance is the second stage input
capacitance or 11*4 + 2 pF plus wiring capacitance, plus first
stage plate capacitance (1 pF), for a total of about 52pF. This
produces a high frequency pole at 300 kHz. The output resistance
is 7.2k paralleled with 12k paralleled with 31.7k or 3.94k. The
capacitance is about 110 pf, dominated by the assumed load
capacitance as specified above. This produces a third high
frequency pole at 380 kHz.
Summary: 1 pole at 300kHz, 1 pole at 380kHz, 1 pole at 600kHz.
Amplifier Gain and Frequency Response:
The midband gain is 33 dB. This is down by 1 dB at 27 Hz, down
3 dB at 16.5 Hz, and the gain drops to unity at 2.8 Hz. At 2.8 Hz,
there is about 275 degrees phase shift between input and output.
The gain is also down by 1 dB at 160 kHz, down 3 dB at 260 kHz,
and drops to unity at 1.2 MHz. At 1.2 MHz, there is about 230
degrees of phase shift between input and output.
These numbers were obtained very simply by plotting the straight
pole/zeros on semi-log paper, and applying the correction factors
as previously described (3 dB error at the pole, 1 dB an octave
away, 0.3 dB 2 octaves away etc)
Regards,
Steve