hwset12solution

# hwset12solution - [12-1 Solution This ampliers input-output...

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[12-1 Solution] This amplifier’s input-output voltage characteristic contains only first and second- order terms. The second order terms will generate all frequency components of the form: | ± f i ± f j | where i, j { 1 , 2 , 3 } . Thus, the following frequencies will be present at the output of the 2-port: Table 1: Frequency components at the output of the 2-port. Note that the second order nonlinearity will also produce a component at “DC” (not listed below) which will cause a shift in the quiescent point. f 1 = 0.6 MHz f 2 = 1.3 MHz f 3 = 1.5 MHz 2 f 1 = 1.2 MHz 2 f 2 = 2.6 MHz 2 f 3 = 3.0 MHz f 1 + f 2 = 1.9 MHz f 1 + f 3 = 2.1 MHz f 2 + f 3 = 2.8 MHz f 3 - f 1 = 0.9 MHz f 3 - f 2 = 0.2 MHz f 2 - f 1 = 0.7 MHz 1

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[12-3 Solution] a. Single tone input signal: v i = a cos ω t Output voltage is: v o ( t ) = 12 a cos ω t a 3 cos 3 ω t = 12 a cos ω t a 3 ( 3 4 cos ω t + 1 4 cos 3 ω t ) v o ( t ) = (12 a 3 4 a 3 ) cos ω t 1 4 a 3 cos 3 ω t The output component at the fundamental frequency is: v o ( t ) = 12 a (1 1 16 a 2 ) cos ω t. 1 dB compression occurs when: (1 1 16 a 2 ) = 10 1 / 20 or | a | = 1 . 319 . The corresponding input power is: P 1 dB = 1 2 1 . 319 2 50 = 0 . 0174 W 12 . 4 dBm . b. Since there is no second-order nonlinearity in this device ( k 2 = 0 ), only first and third-order terms are present in the output: f 1 , f 2 , 3
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