Common-Source Load Line

Part 5b · Voltage Regulation

Key point: \(R_D\) draws a straight line, \(V_{\mathrm{DS}} = V_{\mathrm{DD}} - I_D R_D\). Q is where that line meets the MOSFET curve. Park it on the flat part.

Source is 0 V. \(k\) is in mA/V². \(|A_v|\) is quoted only in saturation.

1
The resistor picks one point.
\(V_{\mathrm{GS}} = 1.55~\mathrm{V}\), \(V_{\mathrm{DD}} = 5~\mathrm{V}\), \(R_D = 4~\mathrm{k}\Omega\). Q is 3.55 V and 0.361 mA, on the flat part. \(V_{\mathrm{ov}} = 850.0~\mathrm{mV}\). \(|A_v| \approx 3.40~\mathrm{V/V}\).
2
The gate slides Q along the same line.
Same \(R_D\) and \(V_{\mathrm{DD}}\). \(V_{\mathrm{GS}}\) to 1.80 V. Q moves to 2.58 V and 0.605 mA. Still saturation. \(|A_v| \approx 4.40~\mathrm{V/V}\).
3
A larger \(R_D\) raises the gain.
\(V_{\mathrm{DD}} = 12~\mathrm{V}\), \(R_D = 8~\mathrm{k}\Omega\), \(V_{\mathrm{GS}} = 1.35~\mathrm{V}\), \(k = 1.2\). Q is 9.97 V and 0.254 mA, still flat. \(|A_v| \approx 6.24~\mathrm{V/V}\).
4
Triode is the wrong corner.
\(V_{\mathrm{GS}} = 2.40~\mathrm{V}\), \(R_D = 8~\mathrm{k}\Omega\), \(k = 1.5\). Q is at 251.4 mV, left of \(V_{\mathrm{DS,sat}} = 1.70~\mathrm{V}\). \(|A_v|\) is not the gain here.
5
Cutoff sits at the supply.
\(V_{\mathrm{GS}} = 0.45~\mathrm{V}\), below \(V_{\mathrm{th}}\). \(I_D = 0.0~\mu\mathrm{A}\). \(V_{\mathrm{out}} = 5.00~\mathrm{V}\). Not a bias for this stage.

The rose line is the resistor. Square-law is the device. \(g_m = k V_{\mathrm{ov}}\) and \(|A_v| \approx g_m R_D\) only while Q stays in saturation. The .asc matches the knobs.

Load line meets the family

Gold Q is the only point both the FET and \(R_D\) accept

Saturation —

\(V_{\mathrm{GS}}\) (V) \(V_{\mathrm{DD}}\) (V) \(R_D\) (kΩ) \(V_{\mathrm{th}}\) (V) \(k\) (mA/V²)

\(V_{\mathrm{DD}} \rightarrow R_D \rightarrow\) drain

\(I_D\) vs \(V_{\mathrm{DS}}\) · rose load line · gold Q

\(V_{\mathrm{out}}\) vs \(V_{\mathrm{GS}}\)

\(I_D\) vs \(V_{\mathrm{GS}}\) · tangent is \(g_m\)

\(V_{\mathrm{out}}\)—

\(I_D\)—

\(V_{\mathrm{ov}}\)—

\(V_{\mathrm{DS,sat}}\)—

\(g_m\)—

\(|A_v|\)—

\(V_{\mathrm{out}} = V_{\mathrm{DD}} - I_D R_D\)

→ —

\(I_{D,\mathrm{sat}} = \tfrac12 k (V_{\mathrm{GS}}-V_{\mathrm{th}})^2\)

→ —

\(g_m = k V_{\mathrm{ov}}\)

→ —