1. ENEE 303 5th Discussion

2. Contents OTA (Operational Trans-conductance Amplifier)
Differential Amplifier Circuits

3. OTA & Y matrix
𝒊𝟏 𝒊𝟐 = 𝟎 𝟎 𝒈𝒎 𝟎 𝒗𝟏 𝒗𝟐
OTA: Output input relationship. Y matrix.
Thevenin Equivalent Circuit: Voc, Isc, Zth

4. Thevenin’s Equivalent Circuit
Any network with two open terminals can be replaced by a single voltage source (VTH) and a series resistance (ZTH) connected to the open terminals.
How to find VTH ?: Voc
How to find ZTH ?: Voc/Isc
Voc, Isc, Zth

5. Thevenin’s Equivalent Circuit
Voc, Isc, Zth

6. Example: OTA & Thevenin

7. Example: OTA & Thevenin

8. Differential Pair: MOSFET
I in terms of (vb1-vb2)

9. Small-Signal Operation of the MOS Differential Pair
Neglect channel modulation
Because of symmetry, the common source connection acts as virtual ground

10. Differential Pair: BJT
I in terms of (vb1-vb2)

11. Large-Signal Operation of the BJT Differential-Pair
The collector currents are,
The emitter currents are,

12. Small-Signal Analysis of the BJT Differential-Pair
The differential gain is then,
𝒊 𝑪𝟏 ≅ 𝜶𝑰 𝟐 + 𝜶𝑰 𝟐 𝑽 𝑻 𝒗 𝒊𝒅 𝟐 = 𝜶𝑰 𝟐 + 𝒈 𝒎 𝒗 𝒊𝒅 𝟐
𝒊 𝑪𝟐 ≅ 𝜶𝑰 𝟐 − 𝜶𝑰 𝟐 𝑽 𝑻 𝒗 𝒊𝒅 𝟐 = 𝜶𝑰 𝟐 − 𝒈 𝒎 𝒗 𝒊𝒅 𝟐

13. Example: Differential Pair
I in terms of (vb1-vb2)

14. Example: Differential Pair
I in terms of (vb1-vb2)