Chap7_Practice - Problem 7.2 Express the current waveform i...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Problem 7.2 Express the current waveform i ( t ) = − . 2cos ( 6 π × 10 9 t + 60 ◦ ) mA in standard cosine form and then determine the following: (a) Its amplitude, frequency, and phase angle. (b) i ( t ) at t = . 1 ns. Solution: i ( t ) = − . 2cos ( 6 π × 10 9 t + 60 ◦ ) (mA) = . 2cos ( 6 π × 10 9 t + 60 ◦ − 180 ◦ ) (mA) = . 2cos ( 6 π × 10 9 t − 120 ◦ ) (mA) . (a) amplitude = . 2 mA; f = 3 × 10 9 Hz = 3 GHz; φ = − 120 ◦ . (b) i ( . 1 ns ) = . 2cos ( 6 π × 10 9 × . 1 × 10 − 9 − 120 ◦ ) (mA) = . 2cos ( . 6 π − 120 ◦ ) (mA) = . 2cos ( 108 ◦ − 120 ◦ ) (mA) = . 196 mA . Problem 7.8 A multiplier circuit has two input ports, designated v 1 and v 2 , and one output port whose voltage v out is equal to the product of v 1 and v 2 . Assume v 1 = 10cos2 π f 1 t V , v 2 = 10cos2 π f 2 t V , (a) Obtain an expression for v out in terms of the sum and difference frequencies, f s = f 1 + f 2 and f d = f 1 − f 2 . (b) Plot its waveform over the time interval [0, 2 s], given that f 1 = 3 Hz and f 2 = 2 Hz. Solution: (a) v out ( t ) = v 1 ( t ) · v 2 ( t ) = ( 10cos2 π f 1 t )( 10cos2 π f 2 t ) = 100cos2 π f 1 t cos2 π f 2 t . Using the identity cos x cos y = 1 2 [ cos ( x + y )+ cos ( x − y )] , v out ( t ) = 100 2 { cos [ 2 π ( f 1 + f 2 ) t ]+ cos [ 2 π ( f 1 − f 2 ) t ] } = 50 ( cos2 π f s t + cos2 π f d t ) . (b) For f 1 = 3 Hz and f 2 = 2 Hz, v out ( t ) = 50 ( cos10 π t + cos2 π t ) (V) . The plot of v out ( t ) is shown in Fig. P7.8. 4 V 2 V- 2 V- 4 V 1 0.8 0.6 0.4 0.2 v 1 v out t (s) v 2 Figure P7.8: Plots of v 1 ( t ) , v 2 ( t ) and v out ( t ) . Section 7-2: Complex Numbers Problem 7.10 Express the following complex numbers in polar form: (a) z 1 = 3 + j 4 (b) z 2 = − 6 + j 8 (c) z 3 = − 6 − j 4 (d) z 4 = j 2 (e) z 5 = ( 2 + j ) 2 (f) z 6 = ( 3 − j 2 ) 3 (g) z 7 = ( −...
View Full Document

{[ snackBarMessage ]}

Page1 / 9

Chap7_Practice - Problem 7.2 Express the current waveform i...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online