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If the 2.2-nF capacitor of Example 9.3 has an area of
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Fundamentals of Electromagnetics with Engineering Applications
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- The input reactance of an infinitesimal linear dipole of length A/60 and radius a=A/200 is given by Xin = – 120 [In(€/a) — 1] tan(ke) Assuming the wire of the dipole is copper with a conductivity of 5.7 x 10' S/m, determine at f = 1 GHz the (a) loss resistance (b) radiation resistance (c) radiation efficiency (d) VSWR when the antenna is connected to a 50-ohm linearrow_forwardExample Solve the octic polynomial 2x⁸-9x⁷+20x⁶-33x⁵+46x⁴-66x³+80x²-72x+32=0 Solution Divide by x⁴ 2x⁴-9x³+20x²-33x+46-66/x + 80/x² - 72/x³ + 32/x⁴=0 Combine and bring terms 2(x⁴+16/x⁴) - 9(x³+8/x³) +20(x²+4/x²)-33(x+2/x) + 46= 0 Let use substitution Let x+2/x =u (x+2/x)²= u² x²+2x*2/x + 4/x² = u² x²+4/x²= u²-4 (x+2/x)³= x³+8/x³+3x*2/x(x+2/x) u³= x³+8/x²+6u x³+8/x³= u³-6u (x²+4/x²)²= x⁴+2x²*4/x² + 16/x⁴ (u²-4)²= x⁴+16/x⁴ + 8 x⁴+16/x⁴ = (u²-4)²-8 x⁴+16/x⁴ = u⁴-8u²+8 2(u⁴-8u²+8)-9(u³-6u)+20(u²-4)-33u+46=0 Expand and simplify 2u⁴-9u³+4u²+21u-18=0 After checking (u-1)(u-2) Are factors Then 2u²-3u-9=0 u=3, u=-3/2 Assignment question Solve the octic polynomial 2s⁸+s⁷+2s⁶-31s⁴-16s³-32s²-160=0 using the above example question, please explain in detailarrow_forwardb) Another waveform g(t) is defined by =0 t≥0, α>0 otherwise g(t)= At exp(-at) and is plotted in Figure 1 (for representative values of 4 = 1 and α = 1). g(t) 0.4T 0.3+ 0.2 0.1+ 2 0 2 Figure 1 8 c) Show that its amplitude spectrum is |G(@)| = - A (a²+0²)² Describe briefly, with the aid of labelled sketches, how changing a affects the waveform in both the time and frequency domains. d) Deduce the Fourier transform H(@) of h(t) = g(t)+g(t+b)+g(t-b) and calculate its DC amplitude H(0).arrow_forward
- "I need an expert solution because the previous solution is incorrect." An antenna with a radiation impedance of 75+j10 ohm, with 10 ohm loss resistance, is connected to a generator with open-circuit voltage of 12 v and an internal impedance of 20 ohms via a 2/4-long transmission line with characteristic impedance of 75 ohms. (a) Draw the equivalent circuit (b) Determine the power supplied by the generator. (c) Determine the power radiated by the antenna. (d) Determine the reflection coefficient at the antenna terminals.arrow_forward--3/5- b) g(t) = 3 1441 g(t+mT) = g(t) -31 (i) Complex fourier coefficient Cn. (ii) Complex fourier coefficients - real fourier coefficient (the first 5 non-zero terms) of (iii) sketch the amplitude spectrum g(t) |Cal against n. n= -3 ⇒n=3 (labelling the axis).arrow_forwardQ4) (i) Calculate the fourier transform of : h(t) 2T (is) h(t) 2T -T о T 2T ·(-++T). cos2t ost≤T (iii) hro (4) ((-++T). cos otherwisearrow_forward
- Q2)a) consider the Circuit in figure 2 with initial conditions of Vc (o) = 5V, I₁ (o) = 1A, (i) redraw the circuit in the frequency domain using laplace Wansforms. (ii) using this circuit derive an equation for the Voltage across the inductor in the time domain.. 3.12 ww =V/3F ZH (figure 2) d) Solve the following second order differential equation using laplace transforms. d12 + 5 dx 3x=71 dt - with initial conditions x² (0) = 2, α(0) = 1arrow_forwardb) Another periodic waveform is defined by T c) g(t)= T with g(t+mT) = g(t) and m is an integer. (i) Sketch g(t) over two full cycles in the time domain, labelling the axes. (ii) Derive the formulae for the complex Fourier coefficients c₁ for g(t). For a periodic waveform h(t), if its complex Fourier coefficients are T T when n is odd T 2n²² T 4nn when n is even and not zero 4nn please derive the first five non-zero terms of the real Fourier series for h(t).arrow_forwardQ3)α) f(t) = (-+- 1 Isto f(t+mT) = f(t). L+- I Ost ST integer (i) sketch f(t) 2 full cycles time domain. (labelling the axis). (ii) Derive the formula for the real fourier Coefficients (i) Real Fourier series f(t), first 5 non-terms. an bn for f(t).arrow_forward
- Q3. a) A periodic waveform is defined by T 3 0≤t< f(t) = SIarrow_forwardQ2. a) Sketch the following waveform f(t)=Vo -1/2≤t≤1/2 =0 otherwise and show that its Fourier transform is 2V ωτ ωτ F(s)-sinotsinc) 2 Use this result to sketch a fully labelled graph of the amplitude spectrum of a single square voltage pulse, of amplitude 24V and pulse width 1.4μs, using units of Hz for the frequency axis. (Note: graph paper is not required - a clear, fully-labelled sketch is adequate).arrow_forwardc) Another periodic waveform is defined by 4t g(t)= 0≤tarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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