MOSFET Vthr-Referenced Current Source

This is a MOSFET constant current source using the threshold voltage (Vthr) as a reference. Iout ≈ Vthr / Riset = Vthr / (Rilim + Riadj) This is supposed to be the MOSFET counterpart of 'BJT Vbe-Referred Current Source' but this circuit has an inherent source of error. Ignoring body effect and neglecting channel length modulation the MOSFET characteristic equation is Id = ½ µn·Cox (W/L)(Vgs - Vt)² Vgs = Vt + √[2Id / (µn·Cox · W/L)] For the gate-to-source voltage (Vgs) to be close to the threshold voltage (Vthr) the drain current (Id) should be minimized while the width to length ratio (W/L) must be made as large as possible. If this is complied √[2Id / (µn·Cox · W/L)] ≈ 0 For the saved circuit the reference MOSFET Q1 have threshold voltage of 1 V. It is desired to have an output current of 100 µA. Vthr = 1 V Iout = 100 µA Reference MOSFET Q1 is sized to have a channel width of 300 µm and a channel length of 25 µm. This results to a W/L of 12. W1 = 300 µm L1 = 25 µm W1/L1 = 12 MOSFET Q2 retains its default parameter values. The biasing resistor (Rbias) is chosen to be large so that the drain current of Q1 is just a little above 1 µA. Id1 ≈ 1 µA ≈ Ibias The projected error voltage is then Vthrerr = √[2Id / (µn·Cox · W/L)] Vthrerr = √[2(1 µA) / (20 µA/V²) · 12)] Vthrerr = √[(1/120) V²)] Vthrerr = 91.2870929175276855761616304668 mV just a little lower than 10%. For the saved values the following voltage and currents were obtained Ibias = 1.0810 µA = Id1 Vref = 1.0949 V = Vgs1 Iout = 99.992 µA = Iref This example shows that the circuit is restricted by the large W/L ratio for the reference MOSFET and the need for a large biasing resistor (a hindrance for IC implementation). A better option is the circuit 'CMOS Vgs Self-Referenced Current Source'.