Cascade and cascode amplifiers
- 1. R.M.K. COLLEGE OF ENGINEERING AND TECHNOLOGY SMALL SIGNAL ANALYSIS OF CASCODE AND CASCADE AMPLIFIER Dr.N.G.Praveena Associate Professor/ECE
- 2. Multistage Amplifiers Increase the overall small-signal voltage gain
- 4. VOLTAGE GAIN AV= 𝑽𝑶 𝑽𝑺 -----(1) From the input circuit, 𝐕𝛑𝟏=VS From the output circuit, 𝐕𝐨= - 𝐠𝐦𝟐𝐕𝛑𝟐 (𝑹𝑪 𝑹𝑳) -----(2) Apply KCL to the E2 of the small signal equivalent circuit, 𝐠𝐦𝟏𝐕𝛑𝟏 = 𝐕𝛑𝟐 𝐫𝛑𝟐 + 𝐠𝐦𝟐𝐕𝛑𝟐 𝐠𝐦𝟏𝐕𝐬 = 𝐕𝛑𝟐 𝐫𝛑𝟐 + 𝐠𝐦𝟐𝐕𝛑𝟐 (∴ 𝐕𝛑𝟏=VS) 𝐠𝐦𝟏𝐕𝐬 = 𝐕𝛑𝟐 +𝐠𝐦𝟐 𝐕𝛑𝟐𝐫𝛑𝟐 𝐫𝛑𝟐 (∴ 𝐠𝐦𝟐𝐕𝛑𝟐=β2) 𝒈𝒎𝟏𝑽𝒔 = 𝐕𝛑𝟐(1+β2) 𝐫𝛑𝟐 𝐕𝛑2= 𝐫𝛑𝟐 (𝟏+𝛃𝟐 ) 𝐠𝐦𝟏𝐕𝐒 −−−−−(3) Sub (3) in (2) 𝑽𝟎 = -𝐠𝐦𝟐 𝒓𝝅𝟐 (𝟏+𝜷𝟐 ) 𝒈𝒎𝟏𝑽𝑺(𝑹𝒄 𝑹𝑳) AV= 𝑽𝑶 𝑽𝑺 = -𝒈𝒎𝟏𝐠𝐦𝟐 𝒓𝝅𝟐 (𝟏+𝜷𝟐 ) (𝐑𝐜 𝑹𝑳) (using 1)
- 5. Input Resistance (Ri) 𝑹𝒊𝟐 =𝐑𝟐 𝐑𝟑 𝐫𝛑𝟏 Output Resistance VS is set to zero 𝑽𝝅𝟏=0 , gm1𝑽𝝅𝟏=0 , 𝑽𝝅𝟐 = 𝟎 , 𝒈𝒎𝟐𝑽𝝅𝟐 = 𝟎 R0 = 𝐑𝐂 𝐑𝐋
- 7. Analysis of Stage 2 Input Resistance (Ri2) 𝑹𝒊𝟐 = 𝒓𝝅𝟐 Voltage Gain(𝑨𝑽𝟐 ) 𝑨𝑽𝟐 = 𝑽𝑶 𝑽𝝅𝟐 The output voltage at stage 2, 𝑽𝑶= 𝐠𝐦𝟐𝑽𝝅𝟐 (𝑹𝑪 𝑹𝑳) ∴ 𝑨𝑽𝟐 = 𝑽𝑶 𝑽𝝅𝟐 = 𝐠𝐦𝟐 (𝑹𝑪 𝑹𝑳)−−−−(1)
- 8. Analysis of Stage 1 VOLTAGE GAIN(𝑨𝑽𝟏 ) 𝑨𝑽𝟏 = 𝑽π𝟐 𝑽𝝅𝟏 The output voltage at stage 1, 𝑽𝝅𝟐 = 𝒈𝒎𝟏𝑽𝝅𝟏 𝑹𝑪𝟏 𝑹𝒊𝟐 𝑨𝑽𝟏 = 𝑽π𝟐 𝑽𝝅𝟏 = 𝒈𝒎𝟏 𝑹𝑪𝟏 𝑹𝒊𝟐 ------(2) OVERALL VOLTAGE GAIN 𝑨𝑽 = 𝑽𝟎 𝑽𝑺 = 𝑽𝟎 𝑽𝝅𝟐 × 𝑽𝝅𝟐 𝑽𝝅𝟏 × 𝑽𝝅𝟏 𝑽𝑺 -----(3) Apply voltage divider rule at the input, we get 𝑽𝝅𝟏= 𝑹𝒊𝟏 𝑹𝒊𝟏 +𝑹𝑺 𝑽𝑺 𝑽π𝟏 𝑽𝑺 = 𝑹𝒊𝟏 𝑹𝒊𝟏 +𝑹𝑺 -------(4) Sub equation (1),(2) and (4) in equation (3), 𝑨𝑽 = 𝒈𝒎𝟐 𝑹𝑪𝟐 𝑹𝑳 𝒈𝒎𝟏 𝑹𝑪𝟏 𝑹𝒊𝟐 . 𝑹𝒊𝟏 𝑹𝒊𝟏 +𝑹𝑺 𝑨𝑽 = gm1𝐠𝒎𝟐 𝑹𝑪𝟐 𝑹𝑳 𝑹𝑪𝟏 𝑹𝒊𝟐 . 𝑹𝒊𝟏 𝑹𝒊𝟏 +𝑹𝑺
- 9. Input resistance 𝐑𝐢𝟏 = 𝐑𝟏 𝐑𝟐 𝐫𝛑𝟏 Output Resistance VS is set to zero 𝑽𝝅𝟏=0 gm1𝑽𝝅𝟏=0 𝑽𝝅𝟐 = 𝟎 𝒈𝒎𝟐𝑽𝝅𝟐 = 𝟎 R0 = RC2