Circuits

Download Spectrum and Network Measurements by Robert A. Witte PDF

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By Robert A. Witte

This new version of Spectrum and community Measurements permits readers to appreciate the fundamental idea, relate it to measured effects, and observe it while growing new designs.

This complete therapy of frequency area measurements effectively consolidates all of the pertinent thought into one textual content. It covers the idea and perform of spectrum and community measurements in digital structures. It additionally presents thorough insurance of Fourier research, transmission strains, intermodulation distortion, signal-to-noise ratio and S-parameters.

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Example text

1 –T/2 Figure 3-5a T/2 t A single time domain pulse. 8 ● Fourier Transform Relationships 33 X(f) –3/T –2/T –1/T 1/T 2/T 3/T f Figure 3-5b The spectrum of a single pulse. The zero crossings of X(f) are often used as a means of estimating the bandwidth of the pulse. Most of the pulse’s energy is in the main lobe, which exists at frequencies below f ¼ 1/T. As the width of the time domain pulse is decreased, T becomes smaller. In the frequency domain, as T becomes smaller, the first zero crossing moves out to a higher frequency.

If P2 is less than P1, the system has a power gain of less than unity and actually exhibits a loss. When expressed in decibels, the gain is negative. If P1 and P2 are equal, the gain is 1, or in dB, 0 dB. In ratio form, the power loss is LP ¼ P1 =P2 ¼ 1=GP ð2-23Þ LPðdBÞ ¼ 10 logðP1 =P2 Þ ¼ 10 logðl=GP Þ ð2-24Þ Using decibels, A loss is the negative of the corresponding gain, when both are expressed in decibels. For example, a loss of 10 dB is the same as a gain of –10 dB. Voltage Gain Gain can also be expressed using voltage, resulting in voltage gain.

Although it is often implied that there is just one FFT, in reality an entire class of algorithms are commonly referred to as the FFT. An FFT algorithm gains a significant speed advantage over the DFT by carefully selecting and organizing intermediate results. Ignoring finite arithmetic effects, the results are the same whether an FFT or a DFT is used. The number of computations required for a DFT is on the order of N2, where N is the number of samples, or record length. The FFT, on the other hand, requires N log2 N computations (log2 indicates the base 2 logarithm).

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