§5.1 MOSFET threshold and transfer characteristics

Unit 5, Lesson 1: MOSFET threshold and transfer characteristics

Model: ID≈(k/2)(VGS−VT)² for saturation Outcome: Analyze the operating principle, calculate a reference case, identify the limit of the approximation, and plan an independent check.

Physical mechanism

An enhancement-mode NMOS channel begins conducting progressively as gate voltage increases. In a simplified long-channel strong-inversion model, drain current is proportional to squared overdrive. The threshold parameter is model dependent; subthreshold conduction is not zero. A gate is insulated and has extremely small steady input current, but finite dynamic charge and leakage.

Draw the relevant circuit or band diagram and name the source of energy, the signal that controls the result, the return path and the reference directions. A model of an individual element must be used with conservation of current and voltage around the complete circuit. This distinction is critical because a device characteristic measured under one set of bias conditions may not hold with a different load. Describe which parameters are external controls and which are intrinsic or empirical device parameters. In mos transistors and amplifier topologies, an especially important issue is headroom; make it explicit before calculating anything.

Derivation and calculation

Start from ID≈(k/2)(VGS−VT)² for saturation. Explain the assumptions required to use the expression and distinguish DC current, incremental gain, instantaneous waveform, average power and RMS quantities wherever they arise. Write the associated Kirchhoff equations and translate all input data to compatible SI units. Verify that the final expression has the dimensions of the required output. If the expression is nonlinear, first identify the valid region; if it is an incremental result, identify the linearization point. An elegant equation is not proof that the circuit's bias or signal swing permits the result.

Worked example. For k=2 mA/V², VT=1 V and VGS=2 V in ideal saturation, ID≈1 mA. Raising VGS to 3 V gives ID≈4 mA, provided supply and compliance allow.

Two independent checks. First examine the zero-drive or zero-load limit where physically applicable. Second change one stated parameter by 10% while holding the others fixed. Explain the sign of the resulting response from the device physics rather than exclusively from differentiation. If this relation predicts a very large current, voltage gain or output power, inspect the supply, load and dissipation limits. The provided numbers are illustrative and are not claims of verified measured devices.

Limitations and expected departures

Short-channel devices, mobility reduction and channel-length modulation violate the ideal quadratic law.

This is the boundary of the teaching model, not evidence that all equations are unreliable. To judge model quality, identify the dominant neglected effect and whether it becomes important at high frequency, high drive, high temperature, or a specific operating region. Component spread may require using lower and upper device ratings rather than a single nominal value. Record whether an observed deviation is likely to arise from a different bias condition, instrument impedance or a real phenomenon the simple expression omits.

Experimental reasoning

Sweep VGS across VT and explain why the ideal model must be labeled rather than treated as a datasheet predictor.

Before energizing hardware, calculate expected terminal voltages and resistor power dissipation and confirm the fixture uses an isolated current-limited low-voltage supply. Measure from a defined ground and avoid exposing test equipment to uncontrolled potentials. Build a table of controlled inputs, model predictions, observed outputs and measurement uncertainty. A measured curve should have labelled axes and should reveal when the hypothesized relation stops being useful. A single matching value does not validate the whole operating range.

Design analysis and independent validation

Treat mosfet threshold and transfer characteristics as a testable physical claim about headroom. Before selecting components, define the source, load, reference arrows and nominal temperature. Then make two different predictions: one based on ID≈(k/2)(VGS−VT)² for saturation, and another based on a conservation law, an alternative model or a limiting case. If the predictions disagree, do not average the answers. Resolve whether there is a sign error, a unit mistake, a different operating region, or an inaccurate assumption. The specified relation models one aspect of field effect, not every physical detail.

Challenge the nominal circuit by varying threshold spread and source degeneration. Explain which quantity should increase and which should decrease based on region compliance. The fact that a classroom formula gives an answer does not establish that a component can deliver the required power or survive the heat. In this example, an important warning is: Short-channel devices, mobility reduction and channel-length modulation violate the ideal quadratic law. Specify what extra model parameters would be necessary to remove that uncertainty.

For an empirical check, Sweep VGS across VT and explain why the ideal model must be labeled rather than treated as a datasheet predictor. Choose at least five observations over the safe input range, label instruments and units, and record what was controlled rather than inferred. A data point that differs from the model is useful: first test the instrument's loading and connections, then check thermal drift and component tolerances. Explain which observed trend would falsify the original assumption. This is more informative than reporting a nominal error percentage without an uncertainty budget.

Exercises (attempt before consulting references)

Describe the carrier, field or feedback mechanism underlying ID≈(k/2)(VGS−VT)² for saturation and show why the predicted output has its stated sign.
Reproduce the numerical case above using SI units, and calculate the percent change in output when the dominant input parameter rises by 20%.
Identify the operating-region or frequency assumption and test one boundary where the formula would be misleading.
Construct a five-point measurement or numerical sweep based on sweep vgs across vt and explain why the ideal model must be labeled rather than treated as a datasheet predictor.; give axes, expected trend and uncertainty.
Propose a modification that reduces sensitivity to threshold spread and source degeneration. Which cost, efficiency, gain or bandwidth tradeoff does it create?
Compare a nominal condition and a defensible worst case, and state which additional device-specific data would be required before hardware release.

Review standard. A complete solution includes a referenced schematic, units, at least one independent plausibility check, and a clearly separated statement of prediction versus observation. Do not certify a real circuit or safety-critical product solely from these simplified cases.

§5.2 MOSFET triode and saturation operation

Unit 5, Lesson 2: MOSFET triode and saturation operation

Model: ID=k[(VGS−VT)VDS−VDS²/2] in triode Outcome: Analyze the operating principle, calculate a reference case, identify the limit of the approximation, and plan an independent check.

Physical mechanism

The gradual-channel approximation gives two mathematical regions. For VDS below overdrive, an NMOS behaves approximately as a voltage-controlled resistance, with drain current depending on VDS. For VDS at or above overdrive, a long-channel square-law idealization gives a saturating current. These boundaries are conventions of an approximate model, not abrupt physical changes in real devices.

Draw the relevant circuit or band diagram and name the source of energy, the signal that controls the result, the return path and the reference directions. A model of an individual element must be used with conservation of current and voltage around the complete circuit. This distinction is critical because a device characteristic measured under one set of bias conditions may not hold with a different load. Describe which parameters are external controls and which are intrinsic or empirical device parameters. In mos transistors and amplifier topologies, an especially important issue is headroom; make it explicit before calculating anything.

Derivation and calculation

Start from ID=k[(VGS−VT)VDS−VDS²/2] in triode. Explain the assumptions required to use the expression and distinguish DC current, incremental gain, instantaneous waveform, average power and RMS quantities wherever they arise. Write the associated Kirchhoff equations and translate all input data to compatible SI units. Verify that the final expression has the dimensions of the required output. If the expression is nonlinear, first identify the valid region; if it is an incremental result, identify the linearization point. An elegant equation is not proof that the circuit's bias or signal swing permits the result.

Worked example. With k=2 mA/V², overdrive 2 V and VDS=1 V, the triode expression gives ID=3 mA. At VDS=2 V, the saturation expression gives 4 mA.

Two independent checks. First examine the zero-drive or zero-load limit where physically applicable. Second change one stated parameter by 10% while holding the others fixed. Explain the sign of the resulting response from the device physics rather than exclusively from differentiation. If this relation predicts a very large current, voltage gain or output power, inspect the supply, load and dissipation limits. The provided numbers are illustrative and are not claims of verified measured devices.

Limitations and expected departures

The model assumes positive overdrive, negligible body effect and no channel-length modulation.

This is the boundary of the teaching model, not evidence that all equations are unreliable. To judge model quality, identify the dominant neglected effect and whether it becomes important at high frequency, high drive, high temperature, or a specific operating region. Component spread may require using lower and upper device ratings rather than a single nominal value. Record whether an observed deviation is likely to arise from a different bias condition, instrument impedance or a real phenomenon the simple expression omits.

Experimental reasoning

Evaluate the two formulas at the region boundary and confirm continuity of current.

Before energizing hardware, calculate expected terminal voltages and resistor power dissipation and confirm the fixture uses an isolated current-limited low-voltage supply. Measure from a defined ground and avoid exposing test equipment to uncontrolled potentials. Build a table of controlled inputs, model predictions, observed outputs and measurement uncertainty. A measured curve should have labelled axes and should reveal when the hypothesized relation stops being useful. A single matching value does not validate the whole operating range.

Design analysis and independent validation

Treat mosfet triode and saturation operation as a testable physical claim about headroom. Before selecting components, define the source, load, reference arrows and nominal temperature. Then make two different predictions: one based on ID=k[(VGS−VT)VDS−VDS²/2] in triode, and another based on a conservation law, an alternative model or a limiting case. If the predictions disagree, do not average the answers. Resolve whether there is a sign error, a unit mistake, a different operating region, or an inaccurate assumption. The specified relation models one aspect of field effect, not every physical detail.

Challenge the nominal circuit by varying threshold spread and source degeneration. Explain which quantity should increase and which should decrease based on region compliance. The fact that a classroom formula gives an answer does not establish that a component can deliver the required power or survive the heat. In this example, an important warning is: The model assumes positive overdrive, negligible body effect and no channel-length modulation. Specify what extra model parameters would be necessary to remove that uncertainty.

For an empirical check, Evaluate the two formulas at the region boundary and confirm continuity of current. Choose at least five observations over the safe input range, label instruments and units, and record what was controlled rather than inferred. A data point that differs from the model is useful: first test the instrument's loading and connections, then check thermal drift and component tolerances. Explain which observed trend would falsify the original assumption. This is more informative than reporting a nominal error percentage without an uncertainty budget.

Exercises (attempt before consulting references)

Describe the carrier, field or feedback mechanism underlying ID=k[(VGS−VT)VDS−VDS²/2] in triode and show why the predicted output has its stated sign.
Reproduce the numerical case above using SI units, and calculate the percent change in output when the dominant input parameter rises by 20%.
Identify the operating-region or frequency assumption and test one boundary where the formula would be misleading.
Construct a five-point measurement or numerical sweep based on evaluate the two formulas at the region boundary and confirm continuity of current.; give axes, expected trend and uncertainty.
Propose a modification that reduces sensitivity to threshold spread and source degeneration. Which cost, efficiency, gain or bandwidth tradeoff does it create?
Compare a nominal condition and a defensible worst case, and state which additional device-specific data would be required before hardware release.

Review standard. A complete solution includes a referenced schematic, units, at least one independent plausibility check, and a clearly separated statement of prediction versus observation. Do not certify a real circuit or safety-critical product solely from these simplified cases.

§5.3 Common-source amplification

Unit 5, Lesson 3: Common-source amplification

Model: Av≈−gm(RD∥RL) Outcome: Analyze the operating principle, calculate a reference case, identify the limit of the approximation, and plan an independent check.

Physical mechanism

A common-source amplifier creates an inverted output because increasing the gate voltage increases drain current and the drain resistor drop. Gain must be computed after finding a DC bias that places the device in the desired region. The MOS gate can present high DC input resistance but not infinite high-frequency impedance due to capacitances. Channel-length modulation produces a finite ro that reduces gain.

Draw the relevant circuit or band diagram and name the source of energy, the signal that controls the result, the return path and the reference directions. A model of an individual element must be used with conservation of current and voltage around the complete circuit. This distinction is critical because a device characteristic measured under one set of bias conditions may not hold with a different load. Describe which parameters are external controls and which are intrinsic or empirical device parameters. In mos transistors and amplifier topologies, an especially important issue is headroom; make it explicit before calculating anything.

Derivation and calculation

Start from Av≈−gm(RD∥RL). Explain the assumptions required to use the expression and distinguish DC current, incremental gain, instantaneous waveform, average power and RMS quantities wherever they arise. Write the associated Kirchhoff equations and translate all input data to compatible SI units. Verify that the final expression has the dimensions of the required output. If the expression is nonlinear, first identify the valid region; if it is an incremental result, identify the linearization point. An elegant equation is not proof that the circuit's bias or signal swing permits the result.

Worked example. For gm=5 mS, RD=5 kΩ and RL=5 kΩ, the parallel load is 2.5 kΩ and the ideal midband gain is approximately −12.5.

Two independent checks. First examine the zero-drive or zero-load limit where physically applicable. Second change one stated parameter by 10% while holding the others fixed. Explain the sign of the resulting response from the device physics rather than exclusively from differentiation. If this relation predicts a very large current, voltage gain or output power, inspect the supply, load and dissipation limits. The provided numbers are illustrative and are not claims of verified measured devices.

Limitations and expected departures

Including ro and an unbypassed source resistance can substantially reduce the predicted gain.

This is the boundary of the teaching model, not evidence that all equations are unreliable. To judge model quality, identify the dominant neglected effect and whether it becomes important at high frequency, high drive, high temperature, or a specific operating region. Component spread may require using lower and upper device ratings rather than a single nominal value. Record whether an observed deviation is likely to arise from a different bias condition, instrument impedance or a real phenomenon the simple expression omits.

Experimental reasoning

Calculate the unloaded and loaded gain and explain the difference in available output swing.

Before energizing hardware, calculate expected terminal voltages and resistor power dissipation and confirm the fixture uses an isolated current-limited low-voltage supply. Measure from a defined ground and avoid exposing test equipment to uncontrolled potentials. Build a table of controlled inputs, model predictions, observed outputs and measurement uncertainty. A measured curve should have labelled axes and should reveal when the hypothesized relation stops being useful. A single matching value does not validate the whole operating range.

Design analysis and independent validation

Treat common-source amplification as a testable physical claim about headroom. Before selecting components, define the source, load, reference arrows and nominal temperature. Then make two different predictions: one based on Av≈−gm(RD∥RL), and another based on a conservation law, an alternative model or a limiting case. If the predictions disagree, do not average the answers. Resolve whether there is a sign error, a unit mistake, a different operating region, or an inaccurate assumption. The specified relation models one aspect of field effect, not every physical detail.

Challenge the nominal circuit by varying threshold spread and source degeneration. Explain which quantity should increase and which should decrease based on region compliance. The fact that a classroom formula gives an answer does not establish that a component can deliver the required power or survive the heat. In this example, an important warning is: Including ro and an unbypassed source resistance can substantially reduce the predicted gain. Specify what extra model parameters would be necessary to remove that uncertainty.

For an empirical check, Calculate the unloaded and loaded gain and explain the difference in available output swing. Choose at least five observations over the safe input range, label instruments and units, and record what was controlled rather than inferred. A data point that differs from the model is useful: first test the instrument's loading and connections, then check thermal drift and component tolerances. Explain which observed trend would falsify the original assumption. This is more informative than reporting a nominal error percentage without an uncertainty budget.

Exercises (attempt before consulting references)

Describe the carrier, field or feedback mechanism underlying Av≈−gm(RD∥RL) and show why the predicted output has its stated sign.
Reproduce the numerical case above using SI units, and calculate the percent change in output when the dominant input parameter rises by 20%.
Identify the operating-region or frequency assumption and test one boundary where the formula would be misleading.
Construct a five-point measurement or numerical sweep based on calculate the unloaded and loaded gain and explain the difference in available output swing.; give axes, expected trend and uncertainty.
Propose a modification that reduces sensitivity to threshold spread and source degeneration. Which cost, efficiency, gain or bandwidth tradeoff does it create?
Compare a nominal condition and a defensible worst case, and state which additional device-specific data would be required before hardware release.

Review standard. A complete solution includes a referenced schematic, units, at least one independent plausibility check, and a clearly separated statement of prediction versus observation. Do not certify a real circuit or safety-critical product solely from these simplified cases.

§5.4 Source followers and buffering

Unit 5, Lesson 4: Source followers and buffering

Model: Av≈gm RS/(1+gm RS) Outcome: Analyze the operating principle, calculate a reference case, identify the limit of the approximation, and plan an independent check.

Physical mechanism

The common-drain or source-follower topology responds to gate changes with a source change in nearly the same direction. The resulting local feedback limits voltage gain to less than one in the elementary small-signal model but lowers output impedance. Source followers are valuable for driving a moderately resistive load without loading a fragile signal source as severely.

Draw the relevant circuit or band diagram and name the source of energy, the signal that controls the result, the return path and the reference directions. A model of an individual element must be used with conservation of current and voltage around the complete circuit. This distinction is critical because a device characteristic measured under one set of bias conditions may not hold with a different load. Describe which parameters are external controls and which are intrinsic or empirical device parameters. In mos transistors and amplifier topologies, an especially important issue is headroom; make it explicit before calculating anything.

Derivation and calculation

Start from Av≈gm RS/(1+gm RS). Explain the assumptions required to use the expression and distinguish DC current, incremental gain, instantaneous waveform, average power and RMS quantities wherever they arise. Write the associated Kirchhoff equations and translate all input data to compatible SI units. Verify that the final expression has the dimensions of the required output. If the expression is nonlinear, first identify the valid region; if it is an incremental result, identify the linearization point. An elegant equation is not proof that the circuit's bias or signal swing permits the result.

Worked example. For gm=8 mS and RS=1 kΩ, Av≈8/9≈0.889. A large increase in gm gives diminishing improvement as Av approaches one.

Two independent checks. First examine the zero-drive or zero-load limit where physically applicable. Second change one stated parameter by 10% while holding the others fixed. Explain the sign of the resulting response from the device physics rather than exclusively from differentiation. If this relation predicts a very large current, voltage gain or output power, inspect the supply, load and dissipation limits. The provided numbers are illustrative and are not claims of verified measured devices.

Limitations and expected departures

Body effect, ro, finite bias-source impedance and output swing limits all affect real follower behavior.

This is the boundary of the teaching model, not evidence that all equations are unreliable. To judge model quality, identify the dominant neglected effect and whether it becomes important at high frequency, high drive, high temperature, or a specific operating region. Component spread may require using lower and upper device ratings rather than a single nominal value. Record whether an observed deviation is likely to arise from a different bias condition, instrument impedance or a real phenomenon the simple expression omits.

Experimental reasoning

Estimate whether a follower can maintain its bias if the output load current doubles.

Before energizing hardware, calculate expected terminal voltages and resistor power dissipation and confirm the fixture uses an isolated current-limited low-voltage supply. Measure from a defined ground and avoid exposing test equipment to uncontrolled potentials. Build a table of controlled inputs, model predictions, observed outputs and measurement uncertainty. A measured curve should have labelled axes and should reveal when the hypothesized relation stops being useful. A single matching value does not validate the whole operating range.

Design analysis and independent validation

Treat source followers and buffering as a testable physical claim about headroom. Before selecting components, define the source, load, reference arrows and nominal temperature. Then make two different predictions: one based on Av≈gm RS/(1+gm RS), and another based on a conservation law, an alternative model or a limiting case. If the predictions disagree, do not average the answers. Resolve whether there is a sign error, a unit mistake, a different operating region, or an inaccurate assumption. The specified relation models one aspect of field effect, not every physical detail.

Challenge the nominal circuit by varying threshold spread and source degeneration. Explain which quantity should increase and which should decrease based on region compliance. The fact that a classroom formula gives an answer does not establish that a component can deliver the required power or survive the heat. In this example, an important warning is: Body effect, ro, finite bias-source impedance and output swing limits all affect real follower behavior. Specify what extra model parameters would be necessary to remove that uncertainty.

For an empirical check, Estimate whether a follower can maintain its bias if the output load current doubles. Choose at least five observations over the safe input range, label instruments and units, and record what was controlled rather than inferred. A data point that differs from the model is useful: first test the instrument's loading and connections, then check thermal drift and component tolerances. Explain which observed trend would falsify the original assumption. This is more informative than reporting a nominal error percentage without an uncertainty budget.

Exercises (attempt before consulting references)

Describe the carrier, field or feedback mechanism underlying Av≈gm RS/(1+gm RS) and show why the predicted output has its stated sign.
Reproduce the numerical case above using SI units, and calculate the percent change in output when the dominant input parameter rises by 20%.
Identify the operating-region or frequency assumption and test one boundary where the formula would be misleading.
Construct a five-point measurement or numerical sweep based on estimate whether a follower can maintain its bias if the output load current doubles.; give axes, expected trend and uncertainty.
Propose a modification that reduces sensitivity to threshold spread and source degeneration. Which cost, efficiency, gain or bandwidth tradeoff does it create?
Compare a nominal condition and a defensible worst case, and state which additional device-specific data would be required before hardware release.

Review standard. A complete solution includes a referenced schematic, units, at least one independent plausibility check, and a clearly separated statement of prediction versus observation. Do not certify a real circuit or safety-critical product solely from these simplified cases.

§5.5 MOS differential pairs and bias mirrors

Unit 5, Lesson 5: MOS differential pairs and bias mirrors

Model: ID1+ID2≈Itail Outcome: Analyze the operating principle, calculate a reference case, identify the limit of the approximation, and plan an independent check.

Physical mechanism

A differential pair steers current between branches as the input voltage difference varies. The sum remains near the tail-source current when the transistors stay properly biased. A current mirror supplies a reference-controlled current but introduces compliance voltage, mismatch and finite output resistance. Differential operation rejects an ideal common-mode input only under matched components and sufficient headroom.

Draw the relevant circuit or band diagram and name the source of energy, the signal that controls the result, the return path and the reference directions. A model of an individual element must be used with conservation of current and voltage around the complete circuit. This distinction is critical because a device characteristic measured under one set of bias conditions may not hold with a different load. Describe which parameters are external controls and which are intrinsic or empirical device parameters. In mos transistors and amplifier topologies, an especially important issue is headroom; make it explicit before calculating anything.

Derivation and calculation

Start from ID1+ID2≈Itail. Explain the assumptions required to use the expression and distinguish DC current, incremental gain, instantaneous waveform, average power and RMS quantities wherever they arise. Write the associated Kirchhoff equations and translate all input data to compatible SI units. Verify that the final expression has the dimensions of the required output. If the expression is nonlinear, first identify the valid region; if it is an incremental result, identify the linearization point. An elegant equation is not proof that the circuit's bias or signal swing permits the result.

Worked example. If an ideal 2 mA tail is balanced, each branch carries 1 mA. A 10% mismatch in effective device strength can create input-referred offset even at zero differential drive.

Two independent checks. First examine the zero-drive or zero-load limit where physically applicable. Second change one stated parameter by 10% while holding the others fixed. Explain the sign of the resulting response from the device physics rather than exclusively from differentiation. If this relation predicts a very large current, voltage gain or output power, inspect the supply, load and dissipation limits. The provided numbers are illustrative and are not claims of verified measured devices.

Limitations and expected departures

A MOS pair does not share the same exact logistic current law as an ideal BJT pair; device equations differ.

This is the boundary of the teaching model, not evidence that all equations are unreliable. To judge model quality, identify the dominant neglected effect and whether it becomes important at high frequency, high drive, high temperature, or a specific operating region. Component spread may require using lower and upper device ratings rather than a single nominal value. Record whether an observed deviation is likely to arise from a different bias condition, instrument impedance or a real phenomenon the simple expression omits.

Experimental reasoning

Check required drain and source voltage headroom before assuming the tail current remains constant.

Before energizing hardware, calculate expected terminal voltages and resistor power dissipation and confirm the fixture uses an isolated current-limited low-voltage supply. Measure from a defined ground and avoid exposing test equipment to uncontrolled potentials. Build a table of controlled inputs, model predictions, observed outputs and measurement uncertainty. A measured curve should have labelled axes and should reveal when the hypothesized relation stops being useful. A single matching value does not validate the whole operating range.

Design analysis and independent validation

Treat mos differential pairs and bias mirrors as a testable physical claim about headroom. Before selecting components, define the source, load, reference arrows and nominal temperature. Then make two different predictions: one based on ID1+ID2≈Itail, and another based on a conservation law, an alternative model or a limiting case. If the predictions disagree, do not average the answers. Resolve whether there is a sign error, a unit mistake, a different operating region, or an inaccurate assumption. The specified relation models one aspect of field effect, not every physical detail.

Challenge the nominal circuit by varying threshold spread and source degeneration. Explain which quantity should increase and which should decrease based on region compliance. The fact that a classroom formula gives an answer does not establish that a component can deliver the required power or survive the heat. In this example, an important warning is: A MOS pair does not share the same exact logistic current law as an ideal BJT pair; device equations differ. Specify what extra model parameters would be necessary to remove that uncertainty.

For an empirical check, Check required drain and source voltage headroom before assuming the tail current remains constant. Choose at least five observations over the safe input range, label instruments and units, and record what was controlled rather than inferred. A data point that differs from the model is useful: first test the instrument's loading and connections, then check thermal drift and component tolerances. Explain which observed trend would falsify the original assumption. This is more informative than reporting a nominal error percentage without an uncertainty budget.

Exercises (attempt before consulting references)

Describe the carrier, field or feedback mechanism underlying ID1+ID2≈Itail and show why the predicted output has its stated sign.
Reproduce the numerical case above using SI units, and calculate the percent change in output when the dominant input parameter rises by 20%.
Identify the operating-region or frequency assumption and test one boundary where the formula would be misleading.
Construct a five-point measurement or numerical sweep based on check required drain and source voltage headroom before assuming the tail current remains constant.; give axes, expected trend and uncertainty.
Propose a modification that reduces sensitivity to threshold spread and source degeneration. Which cost, efficiency, gain or bandwidth tradeoff does it create?
Compare a nominal condition and a defensible worst case, and state which additional device-specific data would be required before hardware release.

Review standard. A complete solution includes a referenced schematic, units, at least one independent plausibility check, and a clearly separated statement of prediction versus observation. Do not certify a real circuit or safety-critical product solely from these simplified cases.

Unit 5, Lesson 1: MOSFET threshold and transfer characteristics

Physical mechanism

Derivation and calculation

Limitations and expected departures

Experimental reasoning

Design analysis and independent validation

Exercises (attempt before consulting references)

Unit 5, Lesson 2: MOSFET triode and saturation operation

Physical mechanism

Derivation and calculation

Limitations and expected departures

Experimental reasoning

Design analysis and independent validation

Exercises (attempt before consulting references)

Unit 5, Lesson 3: Common-source amplification

Physical mechanism

Derivation and calculation

Limitations and expected departures

Experimental reasoning

Design analysis and independent validation

Exercises (attempt before consulting references)

Unit 5, Lesson 4: Source followers and buffering

Physical mechanism

Derivation and calculation

Limitations and expected departures

Experimental reasoning

Design analysis and independent validation

Exercises (attempt before consulting references)

Unit 5, Lesson 5: MOS differential pairs and bias mirrors

Physical mechanism

Derivation and calculation

Limitations and expected departures

Experimental reasoning

Design analysis and independent validation

Exercises (attempt before consulting references)

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