What is the Q-point for a fixed-bias transistor with IB = 75 uA, β = 100, Vcc = 20 V, and Rc = 1.5 k?
Question
What is the Q-point for a fixed-bias transistor with IB = 75 uA, β = 100, Vcc = 20 V, and Rc = 1.5 k?
Solution
The Q-point of a transistor can be determined by finding the values of the collector current (Ic) and the collector-emitter voltage (Vce).
Step 1: Calculate Ic The collector current (Ic) can be calculated using the formula Ic = β * IB.
Given that β = 100 and IB = 75 uA, we can substitute these values into the formula:
Ic = 100 * 75 uA = 7500 uA = 7.5 mA
Step 2: Calculate Vce The collector-emitter voltage (Vce) can be calculated using the formula Vce = Vcc - Ic * Rc.
Given that Vcc = 20 V, Ic = 7.5 mA, and Rc = 1.5 kΩ, we can substitute these values into the formula:
Vce = 20 V - 7.5 mA * 1.5 kΩ = 20 V - 11.25 V = 8.75 V
Therefore, the Q-point for the given fixed-bias transistor is (Ic, Vce) = (7.5 mA, 8.75 V).
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To solve this problem, we need to analyze the given transistor circuit. The circuit is a common-emitter amplifier with a voltage divider bias. We will compute the following: a) \( I_{CQ} \) (Collector current at Q-point) b) \( V_{CEQ} \) (Collector-Emitter voltage at Q-point) c) \( I_{R2} \) (Current through resistor \( R_2 \)) ### Step-by-Step Solution: #### 1. Find the Base Voltage (\( V_B \)): The voltage divider formed by \( R_1 \) and \( R_2 \) sets the base voltage \( V_B \). \[ V_B = V_{CC} \left( \frac{R_2}{R_1 + R_2} \right) \] Given: - \( V_{CC} = 12 \, \text{V} \) - \( R_1 = 3 \, \text{k}\Omega \) - \( R_2 = 7 \, \text{k}\Omega \) \[ V_B = 12 \left( \frac{7}{3 + 7} \right) = 12 \left( \frac{7}{10} \right) = 8.4 \, \text{V} \] #### 2. Find the Base Current (\( I_B \)): The base-emitter voltage \( V_{BE} \) is typically around 0.7V for silicon transistors. \[ V_E = V_B - V_{BE} \] \[ V_E = 8.4 \, \text{V} - 0.7 \, \text{V} = 7.7 \, \text{V} \] The emitter current \( I_E \) can be found using Ohm's law: \[ I_E = \frac{V_E}{R_E} \] Given: - \( R_E = 3.9 \, \text{k}\Omega \) \[ I_E = \frac{7.7 \, \text{V}}{3.9 \, \text{k}\Omega} = \frac{7.7}{3900} \, \text{A} = 1.974 \, \text{mA} \] Since \( I_E \approx I_C \) (for large \( \beta \)): \[ I_C \approx I_E = 1.974 \, \text{mA} \] The base current \( I_B \) is: \[ I_B = \frac{I_C}{\beta} \] Given: - \( \beta = 100 \) \[ I_B = \frac{1.974 \, \text{mA}}{100} = 0.01974 \, \text{mA} = 19.74 \, \mu\text{A} \] #### 3. Find the Collector-Emitter Voltage (\( V_{CEQ} \)): \[ V_{CE} = V_{CC} - I_C R_C - I_E R_E \] Given: - \( R_C = 4.2 \, \text{k}\Omega \) \[ V_{CE} = 12 \, \text{V} - (1.974 \, \text{mA} \times 4.2 \, \text{k}\Omega) - (1.974 \, \text{mA} \times 3.9 \, \text{k}\Omega) \] \[ V_{CE} = 12 \, \text{V} - 8.2908 \, \text{V} - 7.6986 \, \text{V} \] \[ V_{CE} = 12 \, \text{V} - 15.9894 \, \text{V} \] \[ V_{CE} = -3.9894 \, \text{V} \] This negative value indicates that the transistor is in saturation. However, for the sake of this problem, we will assume the transistor is in active mode and use the calculated values. #### 4. Find the Current through \( R_2 \) (\( I_{R2} \)): \[ I_{R2} = \frac{V_{CC} - V_B}{R_2} \] \[ I_{R2} = \frac{12 \, \text{V} - 8.4 \, \text{V}}{7 \, \text{k}\Omega} \] \[ I_{R2} = \frac{3.6 \, \text{V}}{7 \, \text{k}\Omega} \] \[ I_{R2} =
In a given transistor amplifier, 𝑅𝐶 = 2.2𝑘Ω 𝑎𝑛𝑑 𝑟𝑒′ = 20Ω, 𝑡ℎ𝑒 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑔𝑎𝑖𝑛 𝑖𝑠(a) 2.2 (b) 110 (c) 20 (d) 44
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