Electrical Engineering Assignment: DC Gate Voltage

Problem 2
The DC drain current of the MOSFET in the audio amplifier circuit shown in the figure is 500 µA. Find the lower −3 dB frequency of the circuit. For full credit, show all work including the following:
Solution
Since the DC gate voltage current is 0, the DC voltage at the source terminal can be calculated as
VS = -VGSQ, and the gate to source voltage is determined from
IDQ = IQ = Kn (VGSQ-VTN)2
Alternatively, 0.5 = (0.5) (VGSQ – 1)2 which yields VGSQ = - VS = 2
Therefore, VGSQ = VDD – IDQRD -VS= 5 - (1)(2) - (-2) = 5V
The transistor is therefore biased in the saturation region
The small signal equivalent circuit is shown below
Vo = -gmVgsRD
Since Vgs = Vi, the small signal voltage gain is
Av = Vo/Vi = -gmRD = -(1.414) (2) = 2.828
FL = 1/ 2πRC
= 1 / 2 x π x 602 x 10
= 2.642 x 10-5 Hz
Problem 3
In these questions, “place its break frequency” means that the capacitor value in question is calculated independently of the other break frequencies. In other words, each of the capacitance values is calculated by considering the other capacitances to be short-circuits.
At low frequencies, we use the coupling capacitors C1, C2, and C3
Ic(DC) = (β/ β+1) IE
= (100/101) mA = 0.99mA
Therefore, =100/0.99 x 26mV = 2.626 k Ω
For C1
RTh1 = 10k + [2.55k] = 12.55 k Ω
Therefore, f1 = 1/ (2π RTh1 C1) C1 = 1/ (2πx12.55x103 x20Hz)
= 6.34 x 10 -7
Therefore, C1 = 0.643µF
For C2
In this case, C1 and C3 are shorter:20Hz
f1 = 1/ (2π RTh2 C2)
C2 = 1/ (2π (10k + 10k) x 20Hz)
= 3.97 x 10 -7
Therefore, C2 = 0.397µF
For C3
In this case, C1 and C2 are shorter:200Hz
Where ib = (0 – 1) V/ (10k // 100k) + 2.626k
= RTh3 = 1/ Ix
= - [10k // 100 k] + 2.626/- (101)
= 9.09k + 2.626k/101 = 0.116 k Ω
F3 = 1/ 2 π RTh3 C3
= 1 / 2 π x 0.116 x 103 x 200 Hz = 6.86 x 10-6
right31432500Therefore, C3 = 0.686 µF
Problem 4
A power MOSFET must dissipate 100 Watts of power and will require a heatsink. If the maximum rated junction temperature, T j, max , of the device is 150 °C, the ambient temperature is 25 °C, and the device-to-case thermal resistance is 0.5 °C/W, sketch a thermal equivalent circuit and determine the following:
center5651500
* The MOSFET’s case temperature.
θ dev-case - T amb = P D (θ dev−case + θ case−snk + θ snk−amb )
T case − T amb = P D · (θ case−snk + θ snk−case )
T snk = 25 + (100) (0.5) = 75◦ C
T case = 25 + 100 (1 + 0.5)
= 175◦ C
* The maximum permissible thermal resistance between the case and ambient, θ c-a .
θ dev−case = Tj, max − TOC/PD, rated
Tc-a = θ dev−case (PD, rated) + Tj, max
= 0.5 (100) + 150
= 200◦ C
Problem 5
* A BJT class-AB power amplifier is used as the output stage in a car audio system. A representative circuit is shown in the above figure. Assume that the input signal is large enough to drive both Q n and Q p fully into saturation. We consider four different ways of obtaining significant output power in the questions below.
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