Hello! I've recently been studying Sedra by myself, mostly so I recover some lost knowledge in electronics and I'm stuck in the above mentioned problem, which I've attached to the post. Throughout the post I'll be using the same notation as the book.

I started by ignoring the Early Effect so I can calculate the value of \(g_m\), using

\(g_m = \sqrt{2 \. K' \. \frac{W}{L} \. I_D}\)

resulting in

\(g_{m1} = g_{m2} = 1.55 \. mS\)
\(g_{m3} = g_{m4} = 0.755 \. mS\)

Additionally,
\(r_{o1} = r_{o2} = r_{o3} = r_{o4} = \frac{V'_A \. L}{I_D} = 9 \. k\Omega \)

Using equation (7.28), I can calculate the output resistance of both the amplifier (\(R_{on}\)) and the current source (\(R_{op}\))

\(R_{on} = g_{m2} \. r_{o2} \. r_{o1} = 126 k\Omega \)

\(R_{op} = g_{m3} \. r_{o3} \. r_{o4} = 62.8 k\Omega \)

These resistances form a parallel and the open circuit gain becomes

\(A_{vo} = -g_{m1}(R_{op}||R_{on}) = -65.0 \)

This leads me to my problem, because (from my calculations and reasoning), it's impossible for this amplifier to get the required gain after loading. I wonder if by ignoring the early effect on \(I_D\), I'm making a mistake, since the Early Voltage is quite low at \(V_A = 1.8 V\). There's a second part to this problem, but I'm not worried about it right now.

Hope I made my question clear! If you need further clarifications or editing, feel free to let me know.

 

Why do you assume four transistors in cascode amplifier instead of two?

 

Mostly because I'm not given much information regarding the circuit itself. I did ask myself this question, but given that I'm given infomation on both NMOS and PMOS transistors this seemed like a reasonable assumption. The images pertaining to cascode amplifiers in this chapter also show them in pairs of two, though technically you can have as many as you need.

 

The basics cascode amplifier look like this

And notice that M1 work as CS amplifier and M2 as a CG amplifer. And yor task is to solve for RL resistor value to get voltage gain |100V/V|.

 

Oh, I see! I was picturing the circuit as a cascoded amplifier with a cascoded current source (since we're given both NMOS and PMOS), which we then fed to a load resistor RL, much like this one (without RL).

Another question I'd like to ask is why we don't take into account the Early Effect when calculating the transconductance. I understand this at high early voltages, but now low ones. Is it just to make calculations simple, leaving the complex ones for simulations?

 

I'd like to ask is why we don't take into account the Early Effect when calculating the transconductance

Maybe because we are lazy when we are doing the hand calculations.

 

Yeah, it makes sense to keep it simple even at low early voltages where the effect is more noticeable. Either way, thank you for your help! At least the exercise makes a lot more sense now.

 

So, do not forget to show us your result.

 

Here you go! I got \(R_L=132 k\Omega\) and \(A_{v1}= -7.14 V/V\). The gain looks about right, since this gain is taken before the buffering state which increases the output resistance and thus the overall gain.

 

Sorry for the double post, but I made a mistake and before I was able to upload the new image, my time for editing ran out, so I'll have to post it here.

 

Your solution looks good If you ask me.

 

Yeah, I think so as well. Thanks for clearing this up!