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The values of R10 and R50 are su ciently large 1 1012 so that I"1 I"Ci and I"5 I"Co . If source I"5 is deactivated by setting I5value=0 and I1value is assigned a small value (i.e., 1 mA), then z11 and z21 are determined by (1.10) and (1.12), respectively. <Ex1_9.CIR> is executed and the probe feature of PSpice is used to graphically display the magnitudes and phase angles of z11 and z21 in Fig. 1-11(a). Similarly, I"1 is deactivated and I"5 is assigned a small value (I1value=0, I5value=1mA) to determine the values of z12 and z22 by (1.11) and (1.13), respectively. Execution of <Ex1_9.CIR> and use of the Probe feature of PSpice results in the magnitudes and phase angles of z12 and z22 as shown by Fig. 1-11(b). Example 1.10. Use SPICE methods to determine the h parameters suitable for use with sinusoidal excitation at a frequency of 10 kHz for the frequency-sensitive two-port network of Fig. 1-10(a). The h parameters of (1.16) to (1.19) for sinusoidal steady-state excitation are ratios of phasor voltages and currents; thus the values are complex numbers expressible in polar form as hij hij ij . Connect the sinusoidal voltage source and current source of Fig. 1-10(c) to the network of Fig. 1-10(a). The " netlist code below models the resulting network with parameter-assigned values for I"1 and V5 . Two separate executions of <Ex1_10.CIR> are required to produce the results needed for evaluation of all four h parameters.

Reasons 1. Through an external point, a line can be drawn perpendicular to a given line. 2. Given 3. Perpendiculars form right angles; ^s with a rt./ are rt. ^s. 4. Reflexive property 5. Hy-leg 6. Corresponding parts of > triangles are >. 7. To bisect is to divide into two congruent parts 8. A line perpendicular to a segment and bisecting it is its perpendicular bisector.

EXAMPLE 4.2 Obtain the current in each branch of the network shown in Fig. 4-2 (same as Fig. 4-1) using the mesh current method.

Fig. 1-11

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11.1. Determine the locus of (a) The midpoints of the radii of a given circle (b) The midpoints of chords of a given circle parallel to a given line (c) The midpoints of chords of fixed length in a given circle (d) The vertex of the right angle of a triangle having a given hypotenuse (e) The vertex of an isosceles triangle having a given base (f) The center of a circle which passes through two given points (g) The center of a circle tangent to a given line at a given point on that line (h) The center of a circle tangent to the sides of a given angle 11.2. Determine the locus of (a) A boat moving so that it is equidistant from the parallel banks of a stream (b) A swimmer maintaining the same distance from two floats (c) A police helicopter in pursuit of a car which has just passed the junction of two straight roads and which may be on either one of them (d) A treasure buried at the same distance from two intersecting straight roads 11.3. Determine the locus of (a) a planet moving at a fixed distance from its sun; (b) a boat moving at a fixed distance from the coast of a circular island; (c) plants laid at a distance of 20 ft from a straight row of other plants; (d) the outer extremity of a clock hand. (11.1) (11.1) (11.1)

Fig. 4-2 The currents I1 and I2 are chosen as shown on the circuit diagram. starting at point , 20 5I1 10 I1 I2 0 and around the right loop, starting at point , 8 10 I2 I1 2I2 0 Rearranging terms, 15I1 10I2 20 10I1 12I2 8 4 5 Applying KVL around the left loop,

CHAP. 1]

11.4. Excluding points lying outside rectangle ABCD in Fig. 11-15, find the locus of points which are (a) Equidistant from AD and BC (b) Equidistant from AB and CD (c) Equidistant from A and B (d) Equidistant from B and C (e) 5 units from BC (f) 10 units from AB (g) 20 units from CD (h) 10 units from B

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