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- Nov 28, 2011
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Yes, conductance is the reciprocal of resistance. The formula for conductance (G) is G = I / V (which is the reciprocal of V / I, the formula for resistance).
TRANSconductance is also calculated as I / V but the current and voltage used in the calculation are not in the same circuit. In the case of a valve (or FET), the current is the anode (or drain) current, and the voltage is the grid (or gate) voltage.
Valves and FETs are voltage-driven, that is the grid/gate responds to voltage, but the output is a current that flows into the anode/plate. (This current is converted back into a voltage by the anode/drain resistor.)
The transconductance figure therefore tells you the relationship between the input voltage and the output current, expressed as output_current / input_voltage.
When we're interested in signal amplification, we use lower-case parameter names, i.e. 'g' instead of 'G', to indicate that these figures are not absolute numbers; they relate to small CHANGES, which represent the signal being amplified, and which appear ON TOP OF the DC bias conditions that put the device into the part of its characteristic where it will amplify a signal.
Let's take a typical small-signal voltage amplifier using a triode valve. It has an anode load resistor of 100k and a 200VDC supply. Generally you want the anode to sit at about half the supply voltage, which is 100V, so there will be 100V across the load resistor. That means the quiescent (no-signal) anode current will be 1 mA. These figures aren't directly relevant to transconductance; I'm just trying to set the scene
A valve is biased into its linear region by applying a slightly negative voltage to the grid (at least, that's true of the valves that I've dealt with). In this circuit, a typical triode might want its grid to be biased at -2V (relative to the cathode) to give an anode current of 1 mA.
Now if you apply a small AC voltage to the grid (in addition to the static bias voltage that sets the quiescent DC operating conditions), the anode current will vary in a corresponding way. This will cause the voltage across the load resistor to vary, and therefore the anode voltage will vary. This is amplification.
Say that a gate signal of v = 0.1V RMS causes the anode current to vary by i = 0.03 mA RMS. With a 100k anode load resistor, 0.03 mA RMS corresponds to 3V RMS. So the circuit has a voltage gain of 30 (vout = 3V RMS output for vin = 0.1V RMS input).
The valve's transconductance in this circuit is i / v which is 0.03 mA / 0.1V which is 0.0003 Siemens (also sometimes called 'mho' - 'ohm' written backwards). That is 300 µS (microsiemens). (Different from 300 µs, which is microseconds.)
Well, you asked for it ;-)
TRANSconductance is also calculated as I / V but the current and voltage used in the calculation are not in the same circuit. In the case of a valve (or FET), the current is the anode (or drain) current, and the voltage is the grid (or gate) voltage.
Valves and FETs are voltage-driven, that is the grid/gate responds to voltage, but the output is a current that flows into the anode/plate. (This current is converted back into a voltage by the anode/drain resistor.)
The transconductance figure therefore tells you the relationship between the input voltage and the output current, expressed as output_current / input_voltage.
When we're interested in signal amplification, we use lower-case parameter names, i.e. 'g' instead of 'G', to indicate that these figures are not absolute numbers; they relate to small CHANGES, which represent the signal being amplified, and which appear ON TOP OF the DC bias conditions that put the device into the part of its characteristic where it will amplify a signal.
Let's take a typical small-signal voltage amplifier using a triode valve. It has an anode load resistor of 100k and a 200VDC supply. Generally you want the anode to sit at about half the supply voltage, which is 100V, so there will be 100V across the load resistor. That means the quiescent (no-signal) anode current will be 1 mA. These figures aren't directly relevant to transconductance; I'm just trying to set the scene
A valve is biased into its linear region by applying a slightly negative voltage to the grid (at least, that's true of the valves that I've dealt with). In this circuit, a typical triode might want its grid to be biased at -2V (relative to the cathode) to give an anode current of 1 mA.
Now if you apply a small AC voltage to the grid (in addition to the static bias voltage that sets the quiescent DC operating conditions), the anode current will vary in a corresponding way. This will cause the voltage across the load resistor to vary, and therefore the anode voltage will vary. This is amplification.
Say that a gate signal of v = 0.1V RMS causes the anode current to vary by i = 0.03 mA RMS. With a 100k anode load resistor, 0.03 mA RMS corresponds to 3V RMS. So the circuit has a voltage gain of 30 (vout = 3V RMS output for vin = 0.1V RMS input).
The valve's transconductance in this circuit is i / v which is 0.03 mA / 0.1V which is 0.0003 Siemens (also sometimes called 'mho' - 'ohm' written backwards). That is 300 µS (microsiemens). (Different from 300 µs, which is microseconds.)
Well, you asked for it ;-)
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