A basic common-source potential divider JFET circuit is designed with the following characteristics:

\(V_{DD} = 20V\) (Power Supply)

\(I_{DSS} = 10mA\)

\(I_{DQ} = 3mA\)

\(V_{GS(OFF)} = -3V\)

\(V_{DS} = 7V\)

\(R_2 = 150k\Omega\)

\(R_L = 10k\Omega\)

The \(I_{DQ}\) is not supposed to shift more than +-10% from the aforementioned original value for:

\(I_{DSS} = 10mA +- 2mA\)

\(V_{GS(OFF)} = -3V +- 0.5V\)

Assuming that I were to find the gate voltage (and the missing resistance/voltage values such as R1/RS/Vgs/etc) using the graphical approach only, I have figured that I need to first plot two transconductance curves in the same graph, one when:

[Minimum transconductance]

\(I_{DSS} = 8mA\)

\(V_{GS(OFF)} = -2.5V\)

\(I_{DQ} = 2.7mA\)

And the other when:

[Maximum transconductance]

\(I_{DSS} = 12mA\)

\(V_{GS(OFF)} = -3.5V\)

\(I_{DQ} = 3.3mA\)

With the given details, I can draw the transconductance graph like this as an example (where Q2 = max transconductance, Q1 = min transconductance):

From there, I learned that the slope of both the maximum and minimum transconductance curve will give me the value of the transconductance of the actual \(I_{DQ}\) and \(V_{GSQ}\) of the circuit (\(g_m\) = \(\Delta I_D/\Delta V_{GS}\) = \((I_D_{MAX} - I_D_{MIN})/(V_{GS}_{MAX} - V_{GS}_{MIN})\)).

IDmax = maximum transconductance curve ID q-point

IDmin = minimum transconductance curve ID q-point

Vgsmax = maximum transconductance curve Vgs q-point

Vgsmin = minimum transconductance curve Vgs q-point

1. Is my assumption of the slope of both the maximum and minimum transconductance curve being the transconductance value of the actual drain current/gate-source voltage at q-point? If yes, then what are the following steps I should be looking at in order to find the gate voltage? If not, then where does my mistake lie at? Pointing me in the right direction would be very helpful.

2. My teacher advised me that the bias line does not necessarily have to intersect the Q-point of the maximum and minimum transconductance curve. Why is this the case?

Thank you for reading. This is an assignment, and I am not expecting any direct answer. Just a point in the right direction would suffice, thanks again!

\(V_{DD} = 20V\) (Power Supply)

\(I_{DSS} = 10mA\)

\(I_{DQ} = 3mA\)

\(V_{GS(OFF)} = -3V\)

\(V_{DS} = 7V\)

\(R_2 = 150k\Omega\)

\(R_L = 10k\Omega\)

The \(I_{DQ}\) is not supposed to shift more than +-10% from the aforementioned original value for:

\(I_{DSS} = 10mA +- 2mA\)

\(V_{GS(OFF)} = -3V +- 0.5V\)

Assuming that I were to find the gate voltage (and the missing resistance/voltage values such as R1/RS/Vgs/etc) using the graphical approach only, I have figured that I need to first plot two transconductance curves in the same graph, one when:

[Minimum transconductance]

\(I_{DSS} = 8mA\)

\(V_{GS(OFF)} = -2.5V\)

\(I_{DQ} = 2.7mA\)

And the other when:

[Maximum transconductance]

\(I_{DSS} = 12mA\)

\(V_{GS(OFF)} = -3.5V\)

\(I_{DQ} = 3.3mA\)

With the given details, I can draw the transconductance graph like this as an example (where Q2 = max transconductance, Q1 = min transconductance):

From there, I learned that the slope of both the maximum and minimum transconductance curve will give me the value of the transconductance of the actual \(I_{DQ}\) and \(V_{GSQ}\) of the circuit (\(g_m\) = \(\Delta I_D/\Delta V_{GS}\) = \((I_D_{MAX} - I_D_{MIN})/(V_{GS}_{MAX} - V_{GS}_{MIN})\)).

IDmax = maximum transconductance curve ID q-point

IDmin = minimum transconductance curve ID q-point

Vgsmax = maximum transconductance curve Vgs q-point

Vgsmin = minimum transconductance curve Vgs q-point

1. Is my assumption of the slope of both the maximum and minimum transconductance curve being the transconductance value of the actual drain current/gate-source voltage at q-point? If yes, then what are the following steps I should be looking at in order to find the gate voltage? If not, then where does my mistake lie at? Pointing me in the right direction would be very helpful.

2. My teacher advised me that the bias line does not necessarily have to intersect the Q-point of the maximum and minimum transconductance curve. Why is this the case?

Thank you for reading. This is an assignment, and I am not expecting any direct answer. Just a point in the right direction would suffice, thanks again!

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