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Questions tagged [math]

Questions which may involve math, including calculations about signal levels, the math theory of certain modulations or modes, or anything else.

4
votes
1answer
2k views

What does the Friis transmission equation represent and how is it derived?

I've read that the Friis transmission equation can be applied to calculate path loss in ideal space. However, I'd like to better understand the factors that define it and what it represents, and why ...
13
votes
2answers
3k views

Is free space path loss dependent on frequency?

Free space path loss is calculated as: $$ \left( 4 \pi df \over c \right)^2 $$ The presence of $f$ in this equation means that losses increase with increasing frequency, so there's an inherent ...
5
votes
1answer
189 views

How can I calculate the effects of an LNA, antenna gain, etc. on noise performance?

There are many things I might do enable my station to hear weaker signals that would otherwise be buried in noise. Just a few possibilities: Install a nice LNA Increase antenna gain Reduce feedline ...
9
votes
4answers
19k views

Calculating Antenna Length on the FCC Exam vs. in Reality

I have seen the following formulas for calculating half and quarter wavelength antennas: Formula for $\frac{1}{2}$-wavelength antenna (in free space): \begin{equation} \mathrm{Length~(feet)} = \frac{...
4
votes
2answers
69 views

Accounting for feedlines in noise temperature calculations

In writing an answer to "Use noise figure and gain to calculate weakest signal radio can receive?" I've managed to confuse myself. I believe this much is true: $$ T_\text{eq} =T_1 +{T_2 \over G_1} +{...
9
votes
1answer
301 views

Why is the speed of light rounded to 286 Mm in calculations involving frequencies below 30MHz?

I understand that in order to make the maths simpler, frequency ($f$) is expressed in megahertz (MHz) and the velocity of propagation in free space ($c$) for frequencies above 30 MHz is expressed as ...
6
votes
6answers
4k views

Why is antenna aperture a function of wavelength?

Wikipedia says: It can be shown that the aperture of a lossless isotropic antenna, which by definition has unity gain, is: $$ A_{\mathit{eff}} = \frac {\lambda^2}{4 \pi}$$ We also see this ...
7
votes
1answer
153 views

SWR Measured at the Transmitter versus SWR at the Antenna

It is fairly well understood that due to transmission line losses, the SWR as measured at the transmitter will be less than the SWR at the antenna. Some of the new antenna analyzers and some vector ...
7
votes
1answer
104 views

Why is the neper a useful unit for transmission line calculations?

SWR Measured at the Transmitter versus SWR at the Antenna says the neper is "a more convenient unit for transmission line calculations". Why exactly? What is a neper, and what about it makes it more ...
0
votes
1answer
71 views

What is the equation relating maximum data transfer rates for a given EM bandwidth

I was thinking, since visible light has a much higher EM frequency than radio wave light, its bandwidth also has a far higher max data transmission rate, so people have been researching how to use ...