ECExplain

Troubleshooting

Errors in MOSFET Circuit Analysis

Fix common MOSFET circuit analysis errors: region of operation, threshold voltage, body effect, and small-signal model mistakes for ECE exams.

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Wrong ApproachAssume SaturationSkip V_DS CheckWrong I_DvsCorrect ApproachAssume RegionVerify V_DSCorrect I_D

Topic overview

MOSFET circuit analysis requires correctly identifying the operating region (cutoff, triode, or saturation), applying the right drain current equation, and building an accurate small-signal model. Errors in threshold voltage comparison, V_DS versus V_GS - V_th checks, and body effect handling are extremely common in examinations. This guide covers each mistake with concrete numerical examples.

Common mistakes

Mistake 1: Assuming the MOSFET is in saturation without verifying V_DS >= V_GS - V_th
Why it happens: Students default to the saturation drain current formula I_D = (k_n/2)(V_GS - V_th)^2 for all analysis without first checking whether V_DS satisfies the saturation condition.
Correct approach: Step 1: Assume a region (saturation is a common starting point). Step 2: Compute I_D using the saturation formula. Step 3: Compute V_DS from the circuit using KVL. Step 4: Verify V_DS >= V_GS - V_th. If not, the device is in triode and you must use I_D = k_n [(V_GS - V_th) V_DS - V_DS^2 / 2] and solve again.
Example: Wrong: k_n=2 mA/V^2, V_th=1V, V_GS=3V, V_DD=5V, R_D=5k. Student assumes saturation: I_D = (2m/2)(3-1)^2 = 4 mA. V_DS = 5 - 4m x 5k = -15V. Student ignores the negative V_DS and reports I_D = 4 mA. Correct: V_DS = -15V means the saturation assumption is wrong. The device is in triode. Solve the triode equation with V_DS as the unknown using KVL V_DS = V_DD - I_D x R_D simultaneously.
Mistake 2: Confusing V_GS and V_DS conditions for PMOS versus NMOS
Why it happens: Students apply NMOS conditions (V_GS > V_th positive, saturation when V_DS > V_GS - V_th) directly to PMOS, where all inequalities and signs are reversed.
Correct approach: For PMOS: V_th is negative (typically -1V). The device turns on when V_GS < V_th (i.e., V_GS is more negative than V_th). Saturation condition is V_DS <= V_GS - V_th (both sides are negative numbers). Drain current flows from source to drain, so I_D direction reverses relative to NMOS.
Example: Wrong: PMOS with V_th = -1V. Student checks V_GS > V_th: 0 > -1, concludes device is on and in saturation when V_DS > V_GS - V_th, giving a positive V_DS condition. Correct: PMOS is on when V_GS < V_th: V_GS < -1V. Saturation when V_DS <= V_GS - V_th: e.g., if V_GS = -3V, saturation requires V_DS <= -3 - (-1) = -2V.
Mistake 3: Omitting the body effect in circuits where the source is not connected to the bulk
Why it happens: Students learn the basic MOSFET model with V_SB = 0 and apply it universally. When the source potential is nonzero (common in source-follower and cascode circuits), the threshold voltage increases due to the body effect but students use the original V_th.
Correct approach: The body effect modifies the threshold: V_th = V_th0 + gamma (sqrt(2 phi_F + V_SB) - sqrt(2 phi_F)). When V_SB > 0 (NMOS with source above bulk), V_th increases, reducing V_GS - V_th and therefore reducing drain current. In small-signal analysis, the body effect introduces a dependent current source g_mb v_bs in parallel with the main g_m v_gs source.
Example: Wrong: Source-follower circuit with V_S = 2V, V_B = 0V (bulk grounded). Student uses V_th = 0.8V and computes I_D with V_GS = V_G - 2. Correct: V_SB = V_S - V_B = 2V. Compute V_th = 0.8 + 0.4(sqrt(0.6 + 2) - sqrt(0.6)) = 0.8 + 0.4(1.612 - 0.775) = 0.8 + 0.335 = 1.135V. Use this increased threshold in all subsequent calculations.
Mistake 4: Using r_o = infinity in small-signal analysis when the question specifies lambda (channel-length modulation parameter) is nonzero
Why it happens: Students forget that r_o = 1 / (lambda x I_D) and leave it out of the small-signal model, effectively assuming an ideal current source with infinite output resistance.
Correct approach: Whenever lambda is given in the problem (even a small value like 0.02 V^-1), compute r_o = 1 / (lambda x I_D) and include it in the small-signal model as a resistor from drain to source. For gain calculations in common-source amplifiers, the output resistance is R_D || r_o, not R_D alone.
Example: Wrong: lambda = 0.02 V^-1, I_D = 1 mA, R_D = 10k. Student writes A_v = -g_m x R_D = -g_m x 10k. Correct: r_o = 1 / (0.02 x 1m) = 50k. A_v = -g_m x (R_D || r_o) = -g_m x (10k || 50k) = -g_m x 8.33k.

Debugging tips

  • For every MOSFET problem, write three quantities at the top before any calculation: V_GS, V_th, and V_DS. Then evaluate the two inequalities: V_GS > V_th (on condition) and V_DS vs V_GS - V_th (region condition).
  • After computing I_D, use KVL to find V_DS and verify the assumed region. If the verification fails, redo the calculation with the correct region equation. Never skip the verification step.
  • For PMOS circuits, redraw the circuit with all voltage references flipped or replace all voltages with their negatives before applying NMOS formulas. This prevents sign errors in region conditions.
  • In small-signal analysis, list every parameter the problem provides: g_m, r_o, lambda, C_gs, C_gd. If lambda appears, include r_o. If frequency is given, include capacitive impedances.
  • When body effect is mentioned, compute the new V_th before finding the Q-point. Using the original V_th with V_SB nonzero produces a systematically low I_D estimate.

Exam warnings

  • A very common question pattern gives a circuit, asks you to find I_D, and provides just enough headroom for the device to be in triode rather than saturation. Always verify V_DS >= V_GS - V_th after computing I_D. If this is violated, recalculate with the triode equation.
  • Questions involving cascoded or stacked MOSFETs often have nonzero V_SB for inner devices. If the problem states 'the bulk is connected to ground' and the source of a device is not at ground, body effect applies. Ignoring it leads to wrong I_D and V_th.
  • Small-signal gain questions that include lambda in the device parameters expect r_o in your model. Writing A_v = -g_m R_D when r_o is finite and comparable to R_D loses all marks for the gain calculation.
  • For PMOS questions, watch the direction of current arrows and the sign of V_th in the given data. If V_th is listed as a positive number for a PMOS, the problem may be using the magnitude convention. Clarify and apply the correct sign before computing I_D.