Question of Razavi's Book

cascode current mirror razavi

In the chapter of cascode current mirror (5.2) of Razavi's Book
At the beginning of the chapter of current mirrors. Razavi tell us that they neglected channel length modulation. But in practice this effect results in significant error copying currents, especially if minimum length transistors are used so as to minimize the width and hence the output capacitance of the current source.

My question is why this consideration results in significant errors especially if minimum transistos are used?

Can anyone explain this to me

Because Channel Length Modulation is proportional to what?(channel length ofcourse) so as the length goes down the channel effects goes up and the resistance goes down. If have are having low output impedance mosfets(short channel) you must consider them for accurate results.

could you tell in more detail about the channel effects. And the last part i don't understand very well

for a current source, the output resistance is the larger the better, and this is still useful to the current mirror. It means that, when the output resistance of your current is large, the voltage at the output node will affect the output current little.

Now, let's back to the second chapter of Razavi's book, and refer to equation (2.38), you will find the output resistance of MOS transistor in the saturation region is r0=1/λID

and than, back to equation (2.26), you will find an assumption above the equation:

ΔL/L=λVds.

In the common process, ΔL is a constant, so when you use large L, than small λ will be got, and causes the large output resistance to improve the stability of the current mirror. So when you use the minimum length of the transistor, you can not copy the current very will, since the node voltage affects the output current hugely.

Hi,

Channel Length modulation is predominant when the channel dimensions are low. Low channel dimensions can either refer to scaled transistors or minimum length of channel.......... and this channel length modulation lambda=1/rID.....

regds

One way to correct current mirrors for channel length modulation is use cascode transistors both on the reference current transistor and on the mirror current transistor, so by having the same Vds on both you get exact current mirroring.