Summary and typical values

  The complexity of Figure 3.4 is in most cases unnecessary, as several of the occurring capacitances can be ignored without serious consequences.

With these adjustments we get the small signal equivalent diagram in Figure 3.5. Expressions for the component values are given in the Figure. Note that some alternative expressions are given for the transconductance g_m of the MOS transistor. These expressions are useful if the primary and known quantities are not W/L and V_GS, and they may be derived from (3.1-3.2) and (3.5).

In Table 3.1 we show the values of the occurring constants of a typical 1.0 CMOS process. Note that the channel length modulation factor is not constant. It is almost inversely proportional to the channel length L, besides which it is dependent on both V_GS-V_T (small values result in less ) and V_DS-V_T (small values result in less ). The typical values stated apply to transistors with and .

 

N-channel P-channel SPICE parameter C_OX

568cm²/Vs 163cm²/Vs UO KP

V_T0 0.82V -1.06V VTO

0.73V 0.74V PHI GAMMA

0.094V^-1 0.112V^-1 LAMBDA

C_GSO CGSO

C_GDO CGDO

L_D LD

C_j0 CJ

m 0.43 0.51 MJ

C_jp0 CJSW

mp 0.43 0.51 MJSW

0.68V 0.70V PB

 

  
Figure 3.5: Adjusted small-signal equivalent diagram.

 

Saturation Linear g_m g_mb g_ds c_gs c_gd c_bs c_bd

() Calculated for V_DS=0.

 

Two important parameters are defined for the MOS transistor, ^a) the unity-gain frequency, , and ^b) the maximum voltage amplification, A₀. Consider a MOS transistor operating in saturation used as an amplifier. An input voltage is applied over gate-source, and the output voltage is the drain-source voltage. is defined as the (angular) frequency, at which the current amplification of the amplifier is unity. is calculated as
 
This expression shows, that in order to maximise , we should

1. prefer N-channel transistors to P-channel transistors (),
2. avoid small values for the effective gate voltage, V_GS-V_T, and
3. use minimum channel length.

A₀ is defined as the low frequency amplification of the unloaded MOS amplifier. A₀ may be calculated as follows

In order to maximise A₀, we should

1. select a relatively small value of V_GS-V_T,
2. use a longer channel, as this would imply a smaller value for .

Figure 3.6 show curves of several transistor parameters for both N- and P-channel transistors as a function of the effective gate voltage, . Curves are shown with channel lengths of 1 and 10.

  
Figure 3.6: ^a) Channel length modulation factor , ^b) DC amplification A₀, and ^c) unity-gain frequency for a typical 1.0 CMOS process.