CRYSTALSIM

initializing lattice

Reading Advanced Charts

Lesson 1 of 6·15 min read·+80 XP
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From shape recognition to numerical extraction

Anyone can squint at an I-V curve and see 'it goes up'. Mastery means reading numbers off it: V_th, SS, gm, gds, intrinsic gain, fT. These four numbers compress an entire device's behaviour into a fingerprint you can compare, optimize, and defend.

Key Concept
Transconductance (gm)
How much the drain current responds to a change in gate voltage: gm = ∂I_D/∂V_GS at fixed V_DS, measured in S (siemens) or mA/V. The slope of the transfer curve. High gm = strong amplification.
Key Concept
Output conductance (gds)
How much the drain current changes with drain voltage in saturation: gds = ∂I_D/∂V_DS. Lower is better — flat saturation = ideal current source.
Key Concept
Intrinsic gain (Av)
The maximum voltage gain a single transistor can deliver: Av = gm/gds. Modern crystal devices target Av > 100.
Key Concept
Cutoff frequency (fT)
The frequency at which current gain drops to unity: fT ≈ gm / (2π · C_gs). A device's RF speed limit.

I-V curve regions

Three regions, every time:

- Cutoff (V_GS < V_th): exponential subthreshold leakage. Current ~ nA. Use for OFF state. - Linear (V_DS small): I_D rises ~linearly with V_DS. Use as a voltage-controlled resistor. - Saturation (V_DS > V_GS − V_th): I_D plateaus, controlled mainly by V_GS. Use for amplification and digital ON state.

Diagram · Reference I-V family
interactive
Vds (V)Id (µA)0.51.01.52.050010001500LinearSaturation
Vgs: 1.00 V
Vgs 0 V (cutoff)Vth = 0.5 V1.5 V
Hover the curves to see how the three regions transition. Notice how saturation current grows with V_GS.

Transfer curve & subthreshold swing

A transfer curve sweeps V_GS at fixed V_DS. Plot it on a log-y axis and the subthreshold region becomes a straight line. The inverse of its slope is the subthreshold swing SS, in mV/decade.

SS = ∂V_GS / ∂(log₁₀ I_D) — the lower, the sharper the switch. Room-temperature thermionic limit: 60 mV/dec. Crystal + GAA devices reach 65–75 mV/dec.

Practice — drag the cursors

Drag the three coloured cursors below to mark the threshold voltage, the end of the linear (steep) portion, and the saturation onset. Press Check under each to score yourself (±0.08 V tolerance).

Interactive · Cursor practice
Identify the regions
Score: 0/3
V_GS (V)I_D (mA)0.00.40.81.21.6VTHSLOPESAT
Threshold V_th
Where current first turns on
your: 0.20 V
Linear region end
End of the steep dI/dV slope
your: 0.60 V
Saturation onset
Where the curve flattens
your: 1.35 V
Checkpoint · +5 XP
Transconductance is the slope of which curve?

Power-frequency curves trace dynamic power vs operating frequency. The optimal operating point sits at the knee — beyond it, power scales super-linearly (V_dd has to rise to keep timing). Mastery designers operate just below the knee.

Lesson Summary
  • Identify the three regions of an I-V curve at a glance.
  • Find threshold voltage and subthreshold swing on a transfer curve.
  • Compute transconductance, output conductance, intrinsic gain, and cutoff frequency.
  • Use chart cursors to extract numbers, not just shapes.
Test Your Knowledge · +80 XP
1
Which region of an I-V curve gives an ideal voltage-controlled current source?
2
Subthreshold swing is best measured on which axes?
3
Intrinsic gain Av equals:
4
Cutoff frequency fT is the frequency at which:
5
On a power-frequency curve, the 'knee' marks: