Cascode Amplifier using MOSFET Explained (Cascode Amplifier with Cascode Current Source)

Cascode Amplifier Overview

Introduction to Cascode Amplifier

• The video introduces the concept of the Cascode Amplifier, explaining that it consists of two MOSFET stages: an amplifying transistor in a common source configuration and a cascode transistor in a common gate configuration.

Configuration Details

• The lower transistor (amplifying) is configured as a common source, while the upper transistor (cascode) has its gate terminal acting as ground for AC signals. The output is measured at the drain terminal of the common gate stage.

Benefits of Cascode Configuration

• This configuration offers high output resistance, high intrinsic gain, and large bandwidth. It addresses limitations seen in previous configurations by improving output resistance and thus increasing intrinsic gain.

Understanding Intrinsic Gain

Limitations of Common Source Amplifiers

• In prior discussions, it was noted that the intrinsic gain for common source amplifiers typically ranges from 20 to 50 when biased with an ideal current source. Real-world current sources have finite output resistance which reduces this voltage gain.

Role of Output Resistance

• The cascode configuration enhances intrinsic gain by multiplying the output resistance (r0) through its design. This results in improved performance metrics for integrated circuits.

Small Signal Analysis

Analyzing Output Impedance

• For small signal analysis, DC voltage sources are treated as zero. A test voltage is applied to determine output impedance by calculating the ratio of test voltage to test current.

Circuit Behavior Under Test Conditions

• When input signals are considered zero, certain dependent current sources become inactive (open circuit), allowing for simplified analysis using KCL and KVL equations to derive relationships between currents and voltages within the circuit.

Calculating Output Impedance

Deriving Voltage Relationships

• By establishing relationships between various voltages and currents in the circuit, expressions can be derived that relate Vx (voltage across components), ix (input current), r01, r02, and gm2 (transconductance).

Final Expression for Output Impedance

• The final expression shows that output impedance can be approximated as gm2 times r02 times r01 . This indicates how effectively the cascode stage amplifies resistance based on its own intrinsic gain.

Voltage Gain Calculation

Understanding Trans-conductance

• To find voltage gain, trans-conductance must first be determined. It represents how much output current changes with respect to input signal variations.

Methodology for Finding Trans-conductance

Understanding Output Resistance and Voltage Gain in Cascode Amplifiers

Calculating Output Resistance

• The output resistance of the amplifier can be determined by applying a test voltage at the output while considering the input as 0. The ratio of this test voltage to the test current yields the output resistance, which has already been established for the cascode stage.

Voltage Gain Representation

• Once both output resistance and trans-conductance are identified, the equivalent output stage can be expressed as V_out = -i_0 times r_0 or V_out = -G_m times V_i times r_0 . This indicates that voltage gain is directly related to these parameters.

Finding Trans-Conductance

• To find trans-conductance, connect the drain terminal of the second MOSFET to ground. This configuration allows for analysis of current i_0 , which enters through the drain and exits through the source terminal, maintaining equal current flow.

Applying KCL for Current Analysis

• By applying Kirchhoff's Current Law (KCL) at specific nodes, equations can be formed:

• For one node: i_0 = i_d2 + fracV_ds2r_02

• For another node: i_0 = g_m1 V_gs1 + fracV_ds1r_01

These equations help relate currents and voltages across different components in the circuit.

Comparing Equations for Trans-Conductance

• By comparing derived equations from KCL, it becomes evident that:

• g_m1 V_i = g_m2 V_gs2 + ...

This leads to approximations where terms involving conductances dominate others, simplifying calculations significantly. Ultimately, it shows that overall trans-conductance is approximately equal to g_m1 .

Impact of Load on Voltage Gain

Analyzing Voltage Gain with Resistive Load

• When analyzing voltage gain with a resistive load ( R_D ), it appears in parallel with output resistance ( R_0 ). The resulting voltage gain is approximately equal to G_m R_D, indicating similarity to common source amplifier gains when conditions are met.

Using Active Loads for Improved Gain

Understanding Voltage Gain in Cascode Amplifiers

Output Equivalent Circuit and Voltage Gain

• The voltage gain of the cascode amplifier is expressed as G_m times (R_01 parallel R_02) , where R_01 is the output impedance of the cascode stage and R_02 is the output resistance of the current source.

• For maximum gain, R_02 should be comparable to R_01 . If a p-type MOSFET serves as a current source, it can be replaced by its output resistance in AC analysis.

Impedance Analysis

• In this configuration, since R_01 is significantly greater than R_02 , the voltage gain approximates to G_m1 times R_02 , resembling the intrinsic gain of a common source amplifier. This gain can be enhanced using a cascode current source.

• To analyze the output impedance of the cascode current source, all DC sources are treated as zero for AC analysis. The equivalent impedance from one side includes contributions from transistors M3 and M4, with M4's output resistance denoted as r04 .

Cascode Current Source Configuration

• The second transistor acts as a cascode amplifier, multiplying M4's output resistance by its intrinsic gain: equivalent impedance becomes r03 times g_m3 times r04. This results in an overall resistance termed as R0p.

• When connecting this cascode current source to the amplifier, biasing voltages are applied at various points including transistor M1. For AC analysis, these DC biases act as zeroes and can be substituted with their equivalent output resistances.

Overall Voltage Gain Calculation

• The overall voltage gain for this configuration is approximately given by:

• G_m1 times (R_0n parallel R_0p) = G_m1times (R_0n / 2).

• If both resistances are equal (R_0n = R_0p), then it simplifies further to yield higher gains compared to standard configurations.

Conclusion on Performance Improvements

• Using both a cascode amplifier and a cascode current source significantly enhances voltage gain beyond that achievable with common-source amplifiers featuring active loads.