Math Problem Statement

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Odredite vrijednost ulaznog napona UIN, ako je izlazni napon 5 V. Tranzistor radi u području zasićenja. K = 1 mA/V^2, UTH = 1 V, RD = 5 kΩ, RS = 2 kΩ, UDD = 10 V.

Solution

This problem involves a MOSFET transistor operating in the saturation region. We are asked to find the input voltage UINU_{IN} given the output voltage UOUT=5VU_{OUT} = 5 \, \text{V}.

Given Data:

  • K=1mA/V2K = 1 \, \text{mA/V}^2
  • UTH=1VU_{TH} = 1 \, \text{V} (threshold voltage)
  • RD=5kΩR_D = 5 \, \text{k}\Omega
  • RS=2kΩR_S = 2 \, \text{k}\Omega
  • UDD=10VU_{DD} = 10 \, \text{V}
  • UOUT=5VU_{OUT} = 5 \, \text{V}

Step-by-Step Solution:

  1. Identify the MOSFET operating point:

    Since the transistor is in saturation: ID=K2(UGSUTH)2I_D = \frac{K}{2} \left( U_{GS} - U_{TH} \right)^2 where UGSU_{GS} is the gate-source voltage.

  2. Determine the drain current IDI_D:

    The drain current IDI_D can be expressed in terms of the output voltage UOUTU_{OUT} as: ID=UDDUOUTRD=10V5V5kΩ=5V5000Ω=1mAI_D = \frac{U_{DD} - U_{OUT}}{R_D} = \frac{10 \, \text{V} - 5 \, \text{V}}{5 \, \text{k}\Omega} = \frac{5 \, \text{V}}{5000 \, \Omega} = 1 \, \text{mA}

  3. Use the relationship between UGSU_{GS} and IDI_D:

    From the saturation region equation: ID=K2(UGSUTH)2I_D = \frac{K}{2} \left( U_{GS} - U_{TH} \right)^2 Plugging in the known values: 1mA=1mA/V22(UGS1V)21 \, \text{mA} = \frac{1 \, \text{mA/V}^2}{2} \left( U_{GS} - 1 \, \text{V} \right)^2 Simplifying: 2=(UGS1V)22 = \left( U_{GS} - 1 \, \text{V} \right)^2 Taking the square root: UGS1V=21.414VU_{GS} - 1 \, \text{V} = \sqrt{2} \approx 1.414 \, \text{V} So, UGS1.414V+1V=2.414VU_{GS} \approx 1.414 \, \text{V} + 1 \, \text{V} = 2.414 \, \text{V}

  4. Find UINU_{IN} using UGSU_{GS}:

    The relationship between UINU_{IN} and UGSU_{GS} is given by: UGS=UINIDRSU_{GS} = U_{IN} - I_D \cdot R_S Substituting the values: 2.414V=UIN(1mA2kΩ)2.414 \, \text{V} = U_{IN} - (1 \, \text{mA} \cdot 2 \, \text{k}\Omega) 2.414V=UIN2V2.414 \, \text{V} = U_{IN} - 2 \, \text{V} Therefore, UIN=2.414V+2V=4.414VU_{IN} = 2.414 \, \text{V} + 2 \, \text{V} = 4.414 \, \text{V}

Final Answer:

UIN=4.414VU_{IN} = 4.414 \, \text{V}

Would you like further details on any of these steps? Here are five related questions that could extend this problem:

  1. How would the input voltage UINU_{IN} change if the resistor RSR_S is doubled?
  2. What happens to the output voltage UOUTU_{OUT} if UINU_{IN} is increased by 1 V?
  3. How would the solution change if the transistor was operating in the linear region instead of saturation?
  4. How do temperature changes potentially affect the threshold voltage UTHU_{TH} and the operation of the transistor?
  5. What is the significance of the transconductance parameter KK in MOSFET operation?

Tip: Always verify the operating region of the transistor before proceeding with calculations, as it determines the appropriate equations to use.

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Math Problem Analysis

Mathematical Concepts

Electronic Circuit Analysis
Transistor Theory
MOSFET Saturation Region

Formulas

I_D = K/2 * (U_GS - U_TH)^2
I_D = (U_DD - U_OUT) / R_D
U_GS = U_IN - I_D * R_S

Theorems

MOSFET Operation in Saturation Region

Suitable Grade Level

University Level - Electronics Engineering