Math Problem Statement

Determine the following DC values for the amplifier: (a) VB, (b) VE, (c) IE, (d) IC, (e) VC. The given circuit includes resistors R1 = 22 kΩ, R2 = 4.7 kΩ, RC = 2.2 kΩ, and RE = 1.0 kΩ, with a power supply of VCC = 15 V. The DC Beta (βDC) is 90.

Solution

The image contains a transistor amplifier circuit with labeled resistors, capacitors, and voltage sources. Your task asks for DC values related to the circuit:

DC Values to Determine: (a) VBV_B (Base voltage)
(b) VEV_E (Emitter voltage)
(c) IEI_E (Emitter current)
(d) ICI_C (Collector current)
(e) VCV_C (Collector voltage)

Let's proceed step by step to determine these values.


1. Assumptions and Key Relations

  • This is a common-emitter amplifier with resistive biasing.
  • DC Beta (βDC\beta_{DC}) = 90
  • VCC=15VV_{CC} = 15 \, V
  • R1=22kΩR_1 = 22 \, k\Omega, R2=4.7kΩR_2 = 4.7 \, k\Omega, RC=2.2kΩR_C = 2.2 \, k\Omega, RE=1kΩR_E = 1 \, k\Omega

Key relationships:

  • Base voltage (VBV_B): Voltage divider across R1R_1 and R2R_2
  • Emitter voltage: VE=VBVBEV_E = V_B - V_{BE}, where VBE0.7VV_{BE} \approx 0.7 \, V
  • Emitter current: IEVEREI_E \approx \frac{V_E}{R_E}
  • Collector current: ICIEI_C \approx I_E (since ICIE/(1+β)I_C \approx I_E / (1 + \beta))
  • Collector voltage: VC=VCCICRCV_C = V_{CC} - I_C R_C

2. Calculate DC Values Step-by-Step

(a) VBV_B - Base Voltage

Use the voltage divider rule: VB=VCC×R2R1+R2V_B = V_{CC} \times \frac{R_2}{R_1 + R_2} VB=15V×4.7kΩ22kΩ+4.7kΩV_B = 15 \, V \times \frac{4.7 \, k\Omega}{22 \, k\Omega + 4.7 \, k\Omega} VB=15V×4.726.72.64VV_B = 15 \, V \times \frac{4.7}{26.7} \approx 2.64 \, V


(b) VEV_E - Emitter Voltage

[ V_E = V_B - V_{BE} \approx 2.64 , V - 0.

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Math Problem Analysis

Mathematical Concepts

Ohm's Law
Voltage Divider
Transistor Biasing
Current Calculation in Circuits

Formulas

Voltage Divider Formula: VB = VCC * (R2 / (R1 + R2))
Emitter Voltage: VE = VB - VBE (where VBE ≈ 0.7 V)
Emitter Current: IE = VE / RE
Collector Current: IC ≈ IE
Collector Voltage: VC = VCC - IC * RC

Theorems

Kirchhoff's Voltage Law
Ohm's Law

Suitable Grade Level

Undergraduate level (Electronics)