Studio 3 Review MOSFET as current source Small V DS : Resistor (value controlled by V GS ) Large V DS : Current source (value controlled by V GS ) 1
Simulation Review: Circuit Fixed V GS, Sweep V DS I D V DS
Simulation Review: Result Follows linear R on model only for small V DS I D SLOPE = 1 / R on V DS 3
Small V DS linear R on Simulation Review: Result Medium V DS < V GS - V TH : nonlinear ( triode region) I D Large V DS > V GS - V TH : I D determined (mostly) by V GS ("saturation" region) V DS 4
MOSFET Behavior MOSFET channel behaves differently as the channel drain-source voltage V DS increases: Small V DS : linear V DS -I D relationship (model as R on ) Medium V DS < V GS - V TH : nonlinear ( triode ) relationship Large V DS > V GS - V TH : approximately constant current determined (mostly) by V GS 5
What Changed? Reexamine R on derivation: Apply V GS : inversion layer of mobile charge V GS > V TH FIXED MOBILE 6
Reexamine R on Derivation Calculate mobile channel charge Assumed same voltage along channel Q = Cgs(V GS - V TH ) 7
What Changed: Voltage in V DS Channel Problem: apply V DS (to make current flow) V TH =+1V 8
Example: Apply 1V V DS Voltage drop from gate to channel: 3V at S end... V at D end V TH =+1V Less mobile charge at D end Can't assume same charge density across channel 9
Approach: Divide channel along length x into segments dx Within segment, voltage change negligible Current I D same all along channel (Kirchhoff) "KVL" from source to drain Define V ch (x) voltage in channel vs. position V S = 0 V GS = +3V V DS = +1V dr dr dx 10
Original equation: Length = dx; use V ch (x): Massage Resistance of dx segment R on = dr(x) = dr(x) = 1 W µ n C ox ( L V GS V TH ) 1 W µ n C ox ( dx V V (x) V GS ch TH ) dx ( ) µ n C ox W V GS V ch (x) V TH V S = 0 V GS = +3V V DS = +1V dr dx 11
Voltage drop dv across dx segment Ohm s Law: dv = I D dr Substitute for dr: Massage: dv = I D dx ( ) µ n C ox W V GS V ch (x) V TH µ n C ox W ( V GS V ch (x) V TH )dv = I D dx V S = 0 V GS = +3V V DS = +1V dr dx 1
Limits on V: 0 to V DS V DS Integrate both sides Limits on X: 0 to L µ n C ox W ( V GS V ch (x) V TH )dv = I D dx 0 L 0 x = 0 x = L V S = 0 V GS = +3V V DS = +1V dr dr dx 13
Integral result Evaluate Integrate, evaluate both sides µ n C ox W ( V GS V TH )V V V DS = I D x µ n C ox W ( V GS V TH )V DS V DS TRIODE REGION EQUATION I D = µ n C ox W L = I D L ( V V GS TH )V DS V DS 0 L o 14
Triode region equation: Limit for V DS << V GS - V TH V DS small V DS very small I D = µ n C ox W L ( V V GS TH )V DS V DS Approaches resistive model W I D µ n C ox ( L V V GS TH )V DS 15
Small V DS : How small is small? I D = µ n C ox W L ( V GS V TH )V DS LINEAR IN V DS V DS QUADRATIC IN V DS Compare magnitude of linear, quadratic terms 16
Condition: V GD =V TH Pinchoff Gate-to-channel difference must exceed V TH for mobile charge in channel What is current at pinchoff? V TH =+1V V GD =V TH 17
Current at Pinchoff V GD =V TH V GS - V DS =V TH V DS =V GS - V TH Substitute condition into triode equation I D = µ n C ox W L V V DS DS ( V ( GS V TH )( V GS V TH ) V GS V TH ) V DS = V GS - V TH SATURATION TRIODE 18
Current at Pinchoff Current depends only on V GS (ideally) SATURATION REGION EQUATION I D = µ n C ox W ( L V V GS TH ) V DS = V GS - V TH SATURATION TRIODE 19
Beyond Pinchoff (Simplest Model) Higher V DS No additional mobile charge in channel No increase in current V TH =+1V 0
Behavior Current source, controlled by V GS "Saturation region" (will be used as amplifier) V DS = V GS - V TH SATURATION TRIODE 1
Summary: NMOS V DS > V GS - V TH SATURATION V GS - V TH I D = µ nc ox V GS = V GS - V TH W L V GS V TH ( ) V GS > V TH V DS < V GS - V TH TRIODE I D = µ n C ox W L ( V V GS TH )V DS V DS V GS < V TH CUTOFF Analysis strategy: Assume / guess operating region, check for consistency
Summary: PMOS V DS < V GS - V TH SATURATION V GS - V TH I D = µ nc ox V GS = V GS - V TH W L V GS V TH ( ) V GS < V TH V DS > V GS - V TH TRIODE I D = µ n C ox W L ( V V GS TH )V DS V DS V GS > V TH CUTOFF Positive current flows out of drain V GS, V DS negative 3
Lab Exercise: Schematic Display I D - V DS plot on scope 4
Lab Exercise: V-I plot 1 / r o r o Note V DS dependence in active region Not accounted for in simple model 5
Beyond Pinchoff (Reality) Higher V DS Pinchoff point moves toward S Effective channel length L' < L "Channel Length Modulation" I D influenced by V DS L' V TH =+1V 6
Lab Exercise: Scope V-I plot r o r o Try different values of V GS Note what changes, what doesn t in output characteristic Note: If you try to save the scope image to a USB stick and you get a message Control is inactive in XY mode use the Utility > Options > Printer Setup menu and be sure the PRIBT Button function is set to Saves Image To File 7
Data analysis extra : MATLAB Use Saves All To Files option in YT mode to save V DS, I D data to.csv file MATLAB code online to fit parameters 8