# Telescopic Two-Stage Cascode Differential Op-Amp

#### Overview

We designed a fully-differential, telescopic cascode operational amplifier with common-mode feedback. Within the various op-amp topologies, there are numerous tradeoffs between gain, power-consumption, and overall ease of implementation which we had to balance out. To maximize gain and minimize power consumption, we used the telescopic cascode topology.

#### Device Parameters

#### Operating Points

#### Design Process

Our design process for this project took multiple iterations to work as expected. The first design we opted for was a one-stage op-amp, but after testing the intrinsic gain of this configuration, we produced a value of only 40 V/V which is far too small for the minimum gain of 60 dB. As a result, we pivoted our approach to the single stage cascode. In this design, our intrinsic gain slightly improved, but we were still notably short of the minimum open-loop gain. We then pivoted to our final design of our telescopic op amp with a 2 stage cascode to solve this issue as the gain was much higher as shown in Equation 1. Additionally, another benefit of the telescopic topology is that it has a lower power consumption in respect to the 2-stage topology.

To calculate our (W/L) ratios, we used Equation 2 and assumed Voverdrive = 0.2 V to get ID.

After calculating the correct ID value, we were able to calculate the appropriate (W/L) ratios to put our devices into saturation.

To bias our amplifier, we implemented a common-mode feedback circuit from the Gray and Meyer textbook as shown below. In the second stage of the amplifier, the DC voltage is extremely unreliable and susceptible to stability issues in regards to changes in temperature, power supply voltages, etc. By implementing the common-mode circuit, there are two differential pairs which control the tail current of the amplifier and stabilize the DC operating points in the amplifier.

#### Results

Open Loop gain of 60 dB

Closed Loop gain of 4 V/V

Phase Margin of > 60 degrees

Transient Simulation of DC Current from VDD