11.4 Small-signal models and analysis

Transistors are the building blocks of modern electronics. Small-signal models help us understand how they work in real circuits. These models simplify complex transistor behavior, making it easier to analyze and design amplifiers and other circuits.

Small-signal analysis is crucial for predicting how transistors behave with small changes in voltage or current. We'll look at key parameters like transconductance and resistance, and explore how transistors respond to different frequencies. This knowledge is essential for designing effective BJT circuits.

Transistor Small-Signal Models

Hybrid-π Model and T-Model

Top images from around the web for Hybrid-π Model and T-Model

• 

  transistors - How do the hybrid-pi models between N-channel and P-channel JFETs differ ... View original

  Is this image relevant?

• 

  Hybrid \$\pi\$ Model vs. T-Model Input Resistance (MOSFET) - Electrical Engineering Stack Exchange View original

  Is this image relevant?

• 

  transistors - How do the hybrid-pi models between N-channel and P-channel JFETs differ ... View original

  Is this image relevant?

• 

  transistors - How do the hybrid-pi models between N-channel and P-channel JFETs differ ... View original

  Is this image relevant?

• 

  Hybrid \$\pi\$ Model vs. T-Model Input Resistance (MOSFET) - Electrical Engineering Stack Exchange View original

  Is this image relevant?

1 of 3

Top images from around the web for Hybrid-π Model and T-Model

• 

  transistors - How do the hybrid-pi models between N-channel and P-channel JFETs differ ... View original

  Is this image relevant?

• 

  Hybrid \$\pi\$ Model vs. T-Model Input Resistance (MOSFET) - Electrical Engineering Stack Exchange View original

  Is this image relevant?

• 

  transistors - How do the hybrid-pi models between N-channel and P-channel JFETs differ ... View original

  Is this image relevant?

• 

  transistors - How do the hybrid-pi models between N-channel and P-channel JFETs differ ... View original

  Is this image relevant?

• 

  Hybrid \$\pi\$ Model vs. T-Model Input Resistance (MOSFET) - Electrical Engineering Stack Exchange View original

  Is this image relevant?

1 of 3

• Hybrid-π model represents a transistor's small-signal behavior
  • Consists of a voltage-controlled current source (gm*vbe) and resistances (rπ and ro)
  • Used for analyzing transistor circuits at low and medium frequencies (audio and RF)
• T-model provides an alternative representation of the transistor's small-signal characteristics
  • Includes a current-controlled current source (α*ib) and resistances (re and rc)
  • Suitable for analyzing transistor circuits at high frequencies (microwave)

AC Equivalent Circuit and Small-Signal Parameters

• AC equivalent circuit simplifies the transistor model for small-signal analysis
  • Replaces the transistor with its small-signal model components (current source, resistances, and capacitances)
  • Allows for the determination of the circuit's frequency response and gain
• Small-signal parameters describe the transistor's behavior under small-signal conditions
  • Transconductance (gm) represents the change in collector current per unit change in base-emitter voltage ($g_m = \frac{\Delta I_C}{\Delta V_{BE}}$)
  • Base-emitter resistance (rπ) models the dynamic resistance of the base-emitter junction ($r_\pi = \frac{\Delta V_{BE}}{\Delta I_B}$)
  • Collector-emitter resistance (ro) represents the output resistance of the transistor ($r_o = \frac{\Delta V_{CE}}{\Delta I_C}$)

Key Transistor Parameters

Transconductance (gm)

• Transconductance (gm) is a measure of the transistor's ability to convert a change in base-emitter voltage to a change in collector current
  • Defined as the ratio of the change in collector current to the change in base-emitter voltage ($g_m = \frac{\Delta I_C}{\Delta V_{BE}}$)
  • Directly proportional to the transistor's collector current (IC) and inversely proportional to the thermal voltage (VT) ($g_m = \frac{I_C}{V_T}$)
  • Higher gm values indicate a greater amplification capability of the transistor

Base-Emitter Resistance (rπ) and Collector-Emitter Resistance (ro)

• Base-emitter resistance (rπ) represents the dynamic resistance of the base-emitter junction
  • Defined as the ratio of the change in base-emitter voltage to the change in base current ($r_\pi = \frac{\Delta V_{BE}}{\Delta I_B}$)
  • Inversely proportional to the transistor's collector current (IC) and directly proportional to the thermal voltage (VT) ($r_\pi = \frac{V_T}{I_C}$)
• Collector-emitter resistance (ro) models the output resistance of the transistor
  • Defined as the ratio of the change in collector-emitter voltage to the change in collector current ($r_o = \frac{\Delta V_{CE}}{\Delta I_C}$)
  • Depends on the Early voltage (VA) and the collector current (IC) ($r_o = \frac{V_A}{I_C}$)
  • Higher ro values indicate a more stable collector current over a range of collector-emitter voltages

Small-Signal Analysis

Frequency Response

• Frequency response characterizes the transistor's behavior across a range of frequencies
  • Determined by analyzing the transistor's small-signal model with capacitances (Cπ and Cμ)
  • Cπ (base-emitter capacitance) and Cμ (base-collector capacitance) introduce frequency-dependent effects
  • At low frequencies, capacitances have minimal impact on the transistor's gain and output
  • As frequency increases, capacitances begin to shunt the small-signal current, reducing the transistor's gain
• Cutoff frequency (fT) is a key parameter in evaluating the transistor's high-frequency performance
  • Defined as the frequency at which the transistor's current gain (β) drops to unity
  • Depends on the transistor's transconductance (gm) and capacitances (Cπ and Cμ) ($f_T = \frac{g_m}{2\pi(C_\pi+C_\mu)}$)
  • Higher fT values indicate better high-frequency performance and faster switching capabilities