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Chapter 7: Problem 27

Design a voltage-divider bias network using a depletion-type MOSFET with \(I_{D S S}=10 \mathrm{~mA}\) and \(V_{P}=-4 \mathrm{~V}\) to have a \(Q\) -point at \(I_{D_{0}}=2.5 \mathrm{~mA}\) using a supply of \(24 \mathrm{~V}\). In addition, set \(V_{G}=4 \mathrm{~V}\) and use \(R_{D}=2.5 R_{S}\) with \(R_{1}=22 \mathrm{M} \Omega\). Use standard values.

Short Answer

Expert verified
For the design of the voltage-divider bias network using standard value resistors, the calculated values should be: \(R_{S}\) = 1.37 kΩ, \(R_{D}\) = 3,43 kΩ, \(R_{2}\) = 1.6 kΩ, \(R_{1}\) = 800 kΩ. However, consider rounding to nearest standard resistor values: \(R_{S}\) = 1.4 kΩ, \(R_{D}\) = 3.5 kΩ, \(R_{2}\) = 1.6 kΩ, \(R_{1}\) = 820 kΩ.

Step by step solution

01

Determine \(R_{S}\)

Use the given \(V_{G}\) and characteristic equation for a depletion-type MOSFET to solve for \(R_{S}\): \(I_{D}=I_{DSS}\left(1-\frac{V_{GS}}{V_P}\right)^2\). Since \(V_{G}\) is given as 4 V and \(V_{GS}\) equals \(V_{G}-R_{S}I_{D_{0}}\), the equation becomes: \(2.5 \mathrm{~mA}=10\mathrm{~mA}\left(1-\frac{4\mathrm{~V}-R_{S}\times2.5\mathrm{~mA}}{-4\mathrm{~V}}\right)^2\). Solve the equation for \(R_{S}\).
02

Calculate \(R_{D}\)

Once you have the value of \(R_{S}\), calculate \(R_{D}\) using the given relationship that \(R_{D}\)=2.5 \times \(R_{S}\).
03

Find \(R_{2}\)

The gate voltage, \(V_{G}\), is the voltage drop across resistor \(R_{2}\). Use Ohm's law to solve for \(R_{2}\): \(R_{2}=\frac{V_{G}}{I_{R2}}\). The current \(I_{R2}\) is \(I_{D0}\), so \(R_{2}=\frac{4V}{2.5mA}\).
04

Calculate \(R_{1}\)

The supply voltage \(V_{DD}\) is the voltage across the combination of \(R_{1}\) and \(R_{2}\). Use Ohm's law to solve for \(R_{1}\): \(R_{1}=\frac{V_{DD}-V_{G}}{I_{R1}}\). The current \(I_{R1}\) is \(10 \times I_{D0} = 25 mA\) so \(R_{1}=\frac{24V-4V}{25mA}\). Compare this to the given \(R_{1}\), and adjust if necessary to fit standard resistor values.
05

Check biasing conditions

Finally, verify if the biasing conditions satisfy \(R_{D}\approx2.5 R_{S}\) and \(V_{G}=4 ~V\) using the standard nearest values. If the conditions are satisfied, the network is correctly designed.

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Most popular questions from this chapter

Design a self-bias network using a JFET transistor with \(I_{D S S}=8 \mathrm{~mA}\) and \(V_{P}=-6 \mathrm{~V}\) to have a \(Q\) -point at \(I_{D_{Q}}=4 \mathrm{~mA}\) using a supply of \(14 \mathrm{~V}\). Assume that \(R_{D}=3 R_{S}\) and use standard values.
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