cv characteristics of mosfet

This circuit shows how voltage division is done using MOSFETs instead of resistive network. The objective can be achieved by distributing the total applied voltage to a string of diode-connected MOSFETs. The gate-to-source (also drain-to-source in this case) voltages of the MOSFETs can be varied by manipulating the attributes of the individual devices. For this particular purpose the simplest parameters to control are the width and length of the channel. With the saved values the power supply voltage is equal to 9 V. It is desired to have the following output voltages: Vout2 = 5 V Vout1 = 2 V The individual gate-to-source voltages then are: Vgs3 = (9 - 5) V = 4 V Vgs2 = (5 - 2) V = 3 V Vgs1 = (2 - 0) V = 2 V Ignoring body effect and neglecting channel length modulation the working equation is Id = ½ µn Cox (W/L)(Vgs - Vt)² In Multisim KP = µnCox Id = ½ KP (W/L)(Vgs - VTO)² For simplicity, the threshold voltage (VTO) of all MOSFETs were set to 1 V. To proceed, a suitable drain current should be set first, this should be as low as possible the actual value depends on specific application. For the saved circuit Id = 100 µA = Id1 = Id2 = Id3 Q1 is selected as a reference device, calculating the channel aspect ratio Id1 = ½ KP1 (W1/L1)(Vgs1 - VTO1)² (L/W)1 = KP1 (Vgs1 - VTO1)² / 2Id1 (L/W)1 = (20 µA/V²) (2 V - 1 V)² / (2 · 100 µA) (L/W)1 = (20 µA/V²) (1 V²) / (200 µA) (L/W)1 = 1 / 10 (W/L)1 = 10 From this result the channel aspect ratios of the other MOSFETs can be determined. Q2 channel aspect ratio Id2 = Id1 ½ KP2 [(W/L)2] (Vgs2 - VTO2)² = ½ KP1 [(W/L)1] (Vgs1 - VTO1)² [(W/L)2] (Vgs2 - VTO2)² = [(W/L)1] (Vgs1 - VTO1)² [(W/L)2] (3 V - 1 V)² = (10)(2 V - 1 V)² [(W/L)2] (2)² = (10)(1)² [(W/L)2] = 10 / 4 = 5 / 2 = 2.5 Q3 channel aspect ratio Id3 = Id1 ½ KP2 [(W/L)3] (Vgs3 - VTO3)² = ½ KP1 [(W/L)1] (Vgs1 - VTO1)² [(W/L)3] (Vgs3 - VTO3)² = [(W/L)1] (Vgs1 - VTO1)² [(W/L)3] (4 V - 1 V)² = (10)(2 V - 1 V)² [(W/L)3] (3)² = (10)(1)² [(W/L)3] = 10 / 9 = 1.1111111111111111111111111111111 Although the width and length of the channels can be arbitrarily sized, the lengths were set to be all equal having a dimension of 20 µm. The widths were scaled using the ratios obtained from the computations above. W1 = W2 = W3 = 20 µm L1 = 10 · W1 = 10 · 20 µm = 20 µm L2 = 10 · W2 = 2.5 · 20 µm = 50 µm L3 = 10/9 · W1 = 10/9 · 20 µm = 22.222222222222222222222222222222 µm Note: If the power supply is varied, the output voltages will not scale in equal proportion. This is because the aspect ratios of the MOSFETs are different. Variant of this circuit with output voltage(s) that scales proportionately with the power supply are in: MOSFET Half-Supply Voltage Generator and TEXAS INSTRUMENTS TLC551/TLC555 CMOS Timer Control And Trigger Reference Voltage Generator .