E E 435 Assignment 2

Amplifiers

Jasmin Ivankovic

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ProblemsI have included the problems here for quick reference, making this report a self-

contained piece for my research notes.

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About / GoalsFor this assignment, I will be researching and drawing conclusions about

operational amplifiers. The following are the tasks and what they aim to teach

me:

● Reading research articles which will give me insights as to how Op Amps

are developing

● Analytically expressing/manipulating Op Amp equations to gain insights

into their underlying characteristics

● Identifying key features between voltage and current Op Amps

● Working out the details of many textbook representations of Op Amps

● Drawing conclusions about why positive feedback is less common in

textbooks when looking at Op Amps

Research Questions The questions here guide my research and help with completing the assignment

in such a way which maximizes learning. These sets of questions are represented

with different headers. The solutions can be found in the following section,

“Research Notes,” and mostly consist of pictures or notes taken from online

sources, including a link as citation. In response, I shall try to examine the cited

material under scrutiny in the same section.

● Initial Questions

○ How do I set up small signal equations for the amplifier in problem 1?

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○ What is a transresistance amplifier?

■ What are the equations for it?

○ What is a common mode feedback circuit?

● Questions After Problem Set

○ What exactly is compensation, and how does it apply to Op Amps?

Solutions / NotesThe answers to the above questions are here.

➢ Research Questions

➢ Setting up small signal equations

○ the following was taken from Dr. Geigers’s lecture 7 slides from the

previous semester

■ this sets an example for making node voltage equations for a

cascode amplifier

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➢ Definition of transresistance amplifier

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After reading the above paragraph on allaboutcircuits.com, I understand the

result found in problem 3. You want a high output resistance because the output

is voltage, and you do not want a huge drop on the device you are connecting

the output to. Similarly, you want the input resistance to be small so that the

current flows without degradation.

➢ Understanding CMFB

○ The following was taken from Dr. Geiger’s Lecture 20 Spring of 2012

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➢ Problem 1 & 2

➢ The following is my attempt at deriving the ss equations for the above

listed amplifier.

○ first I transformed the schematic to a small signal model

○ I derived equations using node voltage

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V x : gm1 ¿

V y :gm3 (V y )+gm1 ¿

V out : gm4 (V y )+gm2¿

gm1 ¿

I worked on this on a white board for a while, here’s a summary of how far I

got. It would take significantly more effort to solve this. This reminds of

solving Laplace’s equations in E & M.

➢ Problem 3

➢ Part A I’m deriving the voltage gain equation in terms of trans-resistance

V out=−RT [V outR2

+V ¿

R1]

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−V ¿

RTR1

=−V out [1+RTR2

]

A=V out

V ¿=

−RTR1

1+RTR2

⮚ Part B What happens if the trans-resistance approaches infinity?

A=−R2R1

➢ Problem 4

➢ Part A I’m deriving an analytical equation for W/L to have the desired

output

IDQ=W2 LμCox¿

WL

= 4mA12μC ox¿¿

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➢ Problem 5 & 6

➢ Design a 5T op amp without the need for a CMFB circuit

➢ http://tnt.etf.bg.ac.rs/~ms1aik/AIC-15_OTA_FD

➢

Conclusions

What was learned

Ultimately, by trying for analytical solutions I found that these calculations

have a high level of complexity and am grateful for the ways that have been

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developed to simplify our lives. There’s much more research for me to be done.

And I am excited by the prospects that this course offers longform.

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