Introduction to Electric Circuits
126 Resonance Solution Using Equation (6.2) f0 = 1/2~rX/(LC) and rearranging it to make C the subject we get C = 1/4~fo2L (squar ...
1 Series resonance 127 Zmi n - _ I I I 0 fo Figure 6.7 I |max :~ 0 fo Figure 6.8 care must therefore be taken when dealing wit ...
128 Resonance Solution ----4 50~ 20mH C I - II Figure 6.10 250mV f l 0 The circuit is shown in Fig. 6.10. At resonance, )Co = 1/ ...
1 Series resonance 129 Since mo = 1/x/(LC), then Q - L/RV'(LC) = ~L/(RV'C), so e = (1/R)[V(L/C)] (6.5) Q is the ratio of induc ...
130 Resonance Figure 6.12 I L I C Jl I O Vo o bandpass filter circuit is shown in Fig. 6.12. A bandpass filter is designed to al ...
1 Series resonance 131 the resistor is also a maximum. Now if the maximum power is PM = IM 2R at f0 then at fl (or f2) the pow ...
132 Resonance Dividing both numerator and denominator by IR we have H = 1,/[1 + j~oL//R + 1/jwCR] H- 1/{1 + j[wL/R- 1/o~CR]} (6. ...
6.2 Parallel resonance 133 6.2 PARALLEL RESONANCE Also in Chapter 4 we saw that under certain conditions the parallel RLC circui ...
134 Resonance Multiplying both sides by [R 2 + (27rfoL)2]//27rf0 C we get R 2 + (27rf0L)2 = L//C (6.19) (2rrfoL) 2= (L/C) - R 2 ...
Example 6.9 6.2 Parallel resonance 135 A coil having an inductance of 200 ~H and a resistance of 50 1) is connected in parallel ...
136 Resonance Dividing the numerator and the denominator by joJCR this becomes Z = (L/CR)/[1 + (LC/jwCR){(1/LC) - w2}] (6.24) No ...
6.3 Self-assessment test 137 Solution 1 From Equation (6.27) the bandwidth is given by B - ~o0/Q(rad S -1) -- fo//Q(Hertz). Ther ...
138 Resonance 16 Give an expression for the resonant frequency of a parallel circuit assuming that the resistance in the circuit ...
6.4 Problems 139 7 A circuit consisting of a coil of inductance 250 mH, having a resistance of 20 lq, in parallel with a variabl ...
140 Resonance capacitor. A resistor of 2 kl~ is connected in series with this parallel circuit and the whole combination is conn ...
7 Nodal and mesh analysis 7.1 INTRODUCTION For circuits which are more complicated than those considered in the previous chapter ...
142 Nodal and mesh analysis 1 0 3 6 0 A row matrix A row matrix has only one row. Thus [X A row matrix is also called a row vect ...
7.2 Matrices 143 Multiplication of matrices Multiplication of two matrices is only possible if the number of rows in one of the ...
144 Nodal and mesh analysis Solution 3 2 A= 5 1 The product of the elements along the diagonal to the right is 3 x 1 = 3. The pr ...
Cofactors The cofactor of an element am,, the minor of the element. 7.2 Matrices 145 in a square matrix is defined to be (-1)m+" ...
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