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Vs W Rsig 0 WHE r R RG R₂ V DD RD Rs S f) Overall voltage gain G, Ro OLE R₁ V₁=2.4V, k -=1.0 mA/V²,V₁=200V, V₁ =15V, Rig 500 S2, R₂ = 1k Ry=5kΩ, Rg=1kΩ,R=1ΜΩ, R,=415kΩ "L DD a) small signal parameters mo b) Draw the small signal circuit for the amplifier c) Input resistance Rin d) Output Resistance Rout e) Voltage gain A₁ = BAZAART

Vs W Rsig 0 WHE r R RG R₂ V DD RD Rs S f) Overall voltage gain G, Ro OLE R₁ V₁=2.4V, k -=1.0 mA/V²,V₁=200V, V₁ =15V, Rig 500 S2, R₂ = 1k Ry=5kΩ, Rg=1kΩ,R=1ΜΩ, R,=415kΩ "L DD a) small signal parameters mo b) Draw the small signal circuit for the amplifier c) Input resistance Rin d) Output Resistance Rout e) Voltage gain A₁ = BAZAART

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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2 cont) please solve last three sub parts with given info:
### Educational Transcription #### Transistor Circuit Calculations 1. **Voltage Calculation (\(V_{G}\)):** \[ V_{G} = V_{DD} \times \frac{R_2}{R_1 + R_2} \] \[ = 15 \times \left(\frac{0.415}{1.415}\right) \] \[ = 4.4 \, \text{V} \] 2. **Current Analysis (\(I_D\)):** - Voltage Source (\(V_S\)): \[ V_S = I_D R_s + I_0 \] - Current (\(I_0\)): \[ I_0 = \frac{k_n}{2} \, (V_{GS} - V_T)^2 \] Solving yields: \[ I_D = 1 \, (4.4 - I_D - 2.4)^2 \] \[ I_D = (2 - I_D) \] Solving quadratic equation: \[ I_D^2 + 4 - 5 I_D = 0 \] \[ I_D = \frac{5 \pm \sqrt{25-16}}{2} = \frac{5 \pm 3}{2} \] \[ I_D = \underline{I_D = 1} \] 3. **Transconductance Calculation (\(g_m\)):** \[ g_m = \sqrt{2 k_n I_D} \] \[ = \sqrt{2 \times 2 \times 1} \] \[ = \underline{4 \, \text{mA/V}} \] 4. **Output Resistance (\(r_0\)):** \[ r_0 = \frac{V_A}{I_D} = \frac{200 \, \text{V}}{1 \, \text{A}} \] \[ r_0 = \underline{200 \, \text{k}\Omega} \] 5. **Small-Signal Equivalent:** - Capacitors act as short circuits in an AC small-signal analysis
Transcribed Image Text:### Educational Transcription #### Transistor Circuit Calculations 1. **Voltage Calculation (\(V_{G}\)):** \[ V_{G} = V_{DD} \times \frac{R_2}{R_1 + R_2} \] \[ = 15 \times \left(\frac{0.415}{1.415}\right) \] \[ = 4.4 \, \text{V} \] 2. **Current Analysis (\(I_D\)):** - Voltage Source (\(V_S\)): \[ V_S = I_D R_s + I_0 \] - Current (\(I_0\)): \[ I_0 = \frac{k_n}{2} \, (V_{GS} - V_T)^2 \] Solving yields: \[ I_D = 1 \, (4.4 - I_D - 2.4)^2 \] \[ I_D = (2 - I_D) \] Solving quadratic equation: \[ I_D^2 + 4 - 5 I_D = 0 \] \[ I_D = \frac{5 \pm \sqrt{25-16}}{2} = \frac{5 \pm 3}{2} \] \[ I_D = \underline{I_D = 1} \] 3. **Transconductance Calculation (\(g_m\)):** \[ g_m = \sqrt{2 k_n I_D} \] \[ = \sqrt{2 \times 2 \times 1} \] \[ = \underline{4 \, \text{mA/V}} \] 4. **Output Resistance (\(r_0\)):** \[ r_0 = \frac{V_A}{I_D} = \frac{200 \, \text{V}}{1 \, \text{A}} \] \[ r_0 = \underline{200 \, \text{k}\Omega} \] 5. **Small-Signal Equivalent:** - Capacitors act as short circuits in an AC small-signal analysis
**Transcription for Educational Website** --- **Circuit Diagram Overview:** The diagram illustrates a common-source amplifier configuration using a MOSFET transistor. Key components include: - **V\_DD**: The supply voltage. - **R\_D, R\_S, R\_G, R\_sig, R\_L, R\_2**: Resistors connected at various points in the circuit. - **C\_S**: A capacitor connected in parallel with R\_S. - **V\_S**: The input voltage source. - **R\_in, R\_out**: Input and output resistance points. - **V\_o**: The output voltage point. **Given Parameters:** - Threshold voltage \( V_t = 2.4V \) - Transconductance parameter \( \frac{1}{2} k'_n \frac{W}{L} = 1.0 \, \text{mA/V}^2 \) - Early voltage \( V_A = 200V \) - Supply voltage \( V_{DD} = 15V \) - Signal resistance \( R_{Sig} = 500\Omega \) - Load resistance \( R_L = 1k\Omega \) - \( R_D = 5k\Omega \), \( R_S = 1k\Omega \), \( R_G = 1M\Omega \), \( R_2 = 415k\Omega \) **Analysis Tasks:** a) **Small Signal Parameters \( g_m, r_o \):** - Determine the transconductance (\( g_m \)) and output resistance (\( r_o \)) of the small signal model. b) **Draw the Small Signal Circuit for the Amplifier:** - Illustrate the equivalent small signal circuit representation for analysis. c) **Input Resistance \( R_{in} \):** - Calculate the equivalent input resistance as seen by the source. d) **Output Resistance \( R_{out} \):** - Calculate the equivalent output resistance of the circuit. e) **Voltage Gain \( A_V = \frac{v_o}{v_i} \):** - Derive the amplifier's voltage gain from input to output. f) **Overall Voltage Gain \( G_V = \frac{v_o}{v_s} \):** - Determine the overall
Transcribed Image Text:**Transcription for Educational Website** --- **Circuit Diagram Overview:** The diagram illustrates a common-source amplifier configuration using a MOSFET transistor. Key components include: - **V\_DD**: The supply voltage. - **R\_D, R\_S, R\_G, R\_sig, R\_L, R\_2**: Resistors connected at various points in the circuit. - **C\_S**: A capacitor connected in parallel with R\_S. - **V\_S**: The input voltage source. - **R\_in, R\_out**: Input and output resistance points. - **V\_o**: The output voltage point. **Given Parameters:** - Threshold voltage \( V_t = 2.4V \) - Transconductance parameter \( \frac{1}{2} k'_n \frac{W}{L} = 1.0 \, \text{mA/V}^2 \) - Early voltage \( V_A = 200V \) - Supply voltage \( V_{DD} = 15V \) - Signal resistance \( R_{Sig} = 500\Omega \) - Load resistance \( R_L = 1k\Omega \) - \( R_D = 5k\Omega \), \( R_S = 1k\Omega \), \( R_G = 1M\Omega \), \( R_2 = 415k\Omega \) **Analysis Tasks:** a) **Small Signal Parameters \( g_m, r_o \):** - Determine the transconductance (\( g_m \)) and output resistance (\( r_o \)) of the small signal model. b) **Draw the Small Signal Circuit for the Amplifier:** - Illustrate the equivalent small signal circuit representation for analysis. c) **Input Resistance \( R_{in} \):** - Calculate the equivalent input resistance as seen by the source. d) **Output Resistance \( R_{out} \):** - Calculate the equivalent output resistance of the circuit. e) **Voltage Gain \( A_V = \frac{v_o}{v_i} \):** - Derive the amplifier's voltage gain from input to output. f) **Overall Voltage Gain \( G_V = \frac{v_o}{v_s} \):** - Determine the overall
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