TABLE OF CONTENTS We present here a proof [1] of certain statements made in Sec. 7.3 for the intrinsic part of a MOS transistor. The continuity equation is, from (7.7.5),
Integrating with respect to distance from the source to a point x in the channel, we obtain
where 
is a dummy variable of integration. Recognizing i(0, t) as ? i S( t) (see the direction of i in Fig. 7.13), and using (7.7.6b) for i( x, t) we obtain, from (L.2),
Multiplying both sides by dx, integrating from x = 0 to x = L, and dividing both sides by L gives
Interchaning the order of integration and differentiation in the second term of the right-hand side, we obtain
The double integral is of the form ? 0 L G( x) dx, where 
Applying integration by parts to ? 0 L G( x) dx, with G and x the two variables involved, we can write (L.5) as follows:
Comparing the first term to the right-hand side of (4.5.7), we see that, in quasi-static operation, this term will produce the same current expressions as in Sec. 4.5, only with a minus sign and with the terminal voltages as functions of time. We can then write (L.6) as
where i T( t) will be of the form of (7.3.12), and
To find i D( t) =
