Analysis of Intermodulation and Frequency Components

Suppose two tones are input to an amplifier. The tones are pure sinusoids with one at frequency 5 GHz and the other at frequency 5.02 GHz. Assume that the transfer characteristic of the amplifier is represented by Vout (please refer to the attachment for details).

List the output frequencies of all 3rd order (those near 15 GHz) and 4th order (those near 20 GHz) signals in ascending order of frequency. Try to be clever in your approach to this problem. It can be done by brute force but there is a better analytical way.

Two sinusoids signals s1 & s2 are at f1 = 5 GHz, f2 = 5.02 GHz respectively.

Amplifier amplifies the combined input {s1 +s2} in a non linear way such that

Signal out s0 = ko + k1(s1+s2) + k2(s1+s2)power2 + k2(s1+s2)power3 + ...........k9(s1+s2)power9

This leads to 3rd order ...

Solution Summary

The mixing of signals and the resultant intermodulation of two pure sine wave signals at 5 and 5.02 GHz through an amplifier are considered. It is shown how to determine the output signals, their frequnecies, these being the 3rd order and 4th order products and harmonics.

A signal consists of rectangular pulses of duration 0.1 ms that arrive at a receiver at random intervals of time.
What is the shape of the spectrum of the signal?
What is the extent of the spectrum in the frequency domain?
What is the unit that is applied to the magnitude of the spectrum?

Table 4-1 contains the cosine frequencycomponents of a Gaussian peak which has a full width at half-height of 1 sec. The unit height equation for such a Gaussian peak is exp[14(ln 2)t^2] where t is time in sec. For each frequency component f with relative amplitude A calculate A cos 2 pi ft for t=0 +/-0.5 +/-1.5 and +/-2.0 sec.

1. For the waveform shown in FIGURE 1 (see attached file), estimate:
(a) the damping factor (you may compare response with a standard chart)
(b) the forced or damped frequency of oscillation
(c) the natural or undamped frequency
2. Complete the following inverse Laplace transforms (see attached files)

For the waveform shown in attached figure, estimate
(a) the damping factor,
(b) the forced or damped frequency of oscillation, and
(c) the natural or undamped frequency.

Please provide necessary explanations leading to the answer.
a. A square wave signal with voltage levels 0 volts and 2.0 volt at a frequency of 1.00 MHz
is multiplied by a sine wave at a frequency of 5.0 MHz. Which of the following frequencies are
present at the output of the multiplier - there may also

A. A signal generator outputs a unipolar square wave with a period of 0.50 ms. The output of the generator is passed through an ideal low pass filter that has a cut off frequency of 4.5 kHz, to a spectrum analyzer. What frequencies would be seen on the spectrum analyzer screen?
b. The signal generator output in part (a)

(a) Explain the relationship between the spectral components indicated above and the corresponding graph showing the motion of the surface of the motor plotted as a function of time. What do they represent?
(b) Given the amplitudes indicated in the above diagram, copy and complete the table below for the amplitude of the vib