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6.15. SOLVED PROBLEMS

  1. Calculate the minimum value of VDS required for an nMOSFET to operate in the pinch-off when VGS = 1 V with VP = −2 V, and IDSS = 10 mA. What would be the corresponding value of ID?

    Solution:

    It is known that for an nMOSFET the VP is a negative number. Hence, the minimum value of VDS required to keep it in saturation is


  2. Two IGFETs are connected in parallel to form a composite IGFET as shown in Fig. 6.42. Obtain the gm of the composite IGFET if the drain current of each IGFET is described as


    Solution:

    Since both IGFETs are connected in parallel, the resulting drain current of the composite IGFET is


    Figure 6.42. Figure 6.42

  3. Obtain the minimum value of VDS of an n-channel JFET operating in the pinch-off region with Vpo = − 4 V, VGS = −2 V, and IDSS = 10 mA. Calculate the corresponding value ID.

    Solution:


  4. Obtain change in the drain current for VDS = 3 V and corresponding change in the VGS from −2 V to −1 V.

    Solution:

    For VGS − 1 V, VP = VGSVDS = −1 V − 3 V = − 4 V.

    Similarly, for VGS = − 2 V, VP = − 2 V −3 V = − 5 V.


  5. Obtain the pinch-off voltage of a p-channel Silicon FET with its width = 2microns, resistivity of 0.1 Ω m, dielectric constant of 12 and mobility of electrons = 0.05 m2/V.s.

    Solution:


  6. What would be the pinch-off voltage of a p-channel Germanium FET with its width = 2micron, resistivity = 0.002 Ωm, dielectric constant of 16 and mobility of electrons = 0.18 m2Vs?

    Solution:



  7. An n-channel JFET has channel length L = 10 μm, channel width w = 100 μm, channel height without any depletion a = 2.5 μm. The donor level of the channel is ND = 1022/m3 and mobility of the electron μn = 0.15 m2/Vs. The depletion width from each side of the gate junction is 0.25 μm. How does this semiconductor bar behave without forward biasing of the gate junction between two ends of the channel length? Refer Fig. 6.43.

    Figure 6.43. Figure 6.43

    Solution:


  8. A JFET at 300 K has electron density ND = 1023/m3, hole density NA = 1025/m3, relative permiability εr = 12, channel length L = 8 × 10−6m, channel height a = 0.2 × 10−6 m, channel width z = 10 × 10−6 m, electron mobility μn = 0.08 m2/V. sec, drain voltage VD = 10 V, and gate VG = −1 V. Calculate; (a) the pinch-off voltage, (b) the pinch-off current, (c) built-in voltage, (d) the drain current, and (e) the saturation drain current at VG = 0.

    Solution:


  9. Both n-channel MOSFETs in Fig. 6.44 are identical and their V-I characteristics are expressed as


    How much dc current flows through the left MOSFET?

    Solution:

    For VGS = 2V, IDS = (VGS − 1)2 mA = 1mA

    Hence, dc current that can flow through the left

    MOSFET = 2 − 1 = 1 mA.

    Figure 6.44. Figure 6.44

  10. Show that the drain current of an nMOS is given by


  11. Calculate the drain current of an nMOS transistor for VGS = 0 V, 1 V, and 2 V with the device parameters as W = 5 μm, L = 1 μm, VDS = 0.1 V, Vth = 1 V, μnCox = 25 μA/V2.

    Solution:

    For VGS = 0 V < Vth = 1 V, channel does not form, ID = 0

    For VGS = 1 V = Vth, channel does not form, ID = 0

    For VGS = 2 V > Vth = 1 V, channel forms and the equation of ID is


  12. For the device parameters given in problem no. 11, obtain the transconductance of an nMOS in the linear and saturation region with VDS = 0.1 V and VDS = 4 V (>>VGS-Vth).

    Solution:


  13. Calculate the mobility of electron in an nMOS transistor with the device parameters as , VGS = 4 V, Vth = 1.99 V, VDS = 4 V, εox = 3.97εo, ID = 144 μA, tox = 400 Å.

    Solution:


  14. In an enhancement mode nMOS the device parameters were given as VGS = 3 V, VDS = 5 V, Vth = 1 V, μnCox = 25 μA / V2, ID = 0.25 mA, find out the value of aspect ratio of the transistor. Also obtain length and width of the channel.

    Solution:


    if we assume L = 1 μm, then W = 2.5 μm.

  15. Obtain ON resistance of an NMOS transistor with VGS = 3 V, Vth = 1 V, μnCox = 25 mA / V2, W = 3 μm, L = 1 μm.

    Solution:



  16. The internal parameters of an nMOS transistor are NA = 1016 / cm3, the concentration of source and drain is ND = 1020 / cm3, the side wall doping = NA(SW) = 5 × 1016 / cm3, oxide layer thickness = tox = 400 Å, the junction depth = 1 μm. Calculate the junction capacitance with and without side wall doping profile.

    Solution:


  17. Determine the small signal parameters of FET for given value of IDSS = 5 mA, VGS = −1 V, Vp = −4 V, Early voltage VA = 90 V.

    Solution:


  18. An enhancement-type nMOS transistor is shown in Fig. 6.45 with its threshold voltage Vth = 2 V.

    Specify its range of operation for (a) VD = 0.5 V, (b) 1 V, (c) 5 V.

    Figure 6.45. Figure 6.45

    Solution:

    (a) VD = VDS = 0.5 V < (VGSVth) = 3 − 2 = 1 V ⇒ Triode region

    (b) VD = VDS = 1 V ≥ (VGSVth) = 3 − 2 = 1 V ⇒ Saturation

    (c) VD = VDS = 5 V ≥ (VGSVth) = 3 − 2 = 1 V ⇒ Saturation

  19. Obtain the value of drain current in Problem 18 if μnCox = 20 μA/V2, W = 100 μm, and L = 10 μm neglecting the dependence of ID over VDS.

    Solution:


  20. An enhancement-type nMOS transistor with voltage Vth = 2 V conducts drain current ID = 1 mA for VGS = VDS = 3 V neglecting dependence of ID over VDS in saturation. Obtain the value of ID for VGS = 4 V and VDS = 5 V. Also calculate the drain to source resistance rd for small value of VDS and VGS = 4 V.

    Solution:



  21. An enhancement-type nMOS transistor with , Vth = 2V and λ = 0.02/V operators at VGS = 4 V. Obtain drain current for VDS = 2V and 5V and the drain resistance at this value of VGS.

    Solution:


  22. An enhancement-type nMOS transistor has COXμn = 20 mA/V2, W = 100 μm, L = 10 μm, VA = 100 V, Vth = 1 V, λ = 0.5 V1/2, and 2φf = 0.6 V. Calculate the value of Vth at VSB = 4 V and also at VGS = 3 V and VDS = 5 V. Obtain drain current ID for VSB = 3 V. What is output resistance ro for each of the two cases?

    Solution:


  23. Obtain minimum rd required to operate in the saturation region with VGS = 1 V in case of a depletion-type nMOS transistor having Vth = −2 V and = 2mA/V2. How much is the corresponding drain current ID?

    Solution:


  24. Obtain the voltage that will appear at the source neglecting the effect of VDS on ID in case of a depletion-type nMOS transistor shown in Fig. 6.46 having Vth = −2V and .

    Solution:


    Figure 6.46. Figure 6.46

    Figure 6.47. Figure 6.47

  25. Design the circuit in Fig. 6.47 to yield a drain current ID of 0.4 mA. Obtain the dc value of VO and the value of R.

    Solution:

    For design parameters, let Vth = 2 V, μnCox = 20 μA/V2, L = 10 μm, and W = 100 μm.

    The channel length modulation is neglected (λ = 0)

    VDG = 0, MOSFET operates in saturation region.



  

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