Questions tagged [math]

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

26 questions
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 ...
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): \mathrm{Length~(feet)} = \frac{...
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 ...
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 ...
238 views

How can the voltage at the center of a resonant half wave dipole be zero if the input impedance is 75 ohms?

If the input impedance of a resonant half wave dipole at the feed point is 75 + j0 ohms, then if an AC sine wave voltage V is applied to the feed point, how can the voltage at the center be zero ? ...
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 ...
338 views

What is dB(μV/m), and what are its applications?

Many radio coverage tools yield results in dB(μV/m). For example, CRC-COVWEB or nearly any tool based on the Longly-Rice model. The unit occurs in regulations sometimes as well. For example, maximum ...
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 ...
6k views

How to find the front-to-back ratio given an antenna radiation pattern diagram?

I know that the front-to-back ratio is 18dB in the below antenna radiation pattern diagram, but I don't know how to read the diagram to obtain this result. How does one read and understand such ...
592 views

How does FM encode BOTH amplitude and frequencies of full audio signal spectrum?

How does frequency modulation encode both amplitude and frequency of the modulating audio signal only by varying frequency? How do both components get spread across and encoded in the side bands? I ...
2k views

Decibel subtraction in dBm and dB

If i have equations for subtraction of 27dBm-3dBm=27dBm how can this be written as 24 dB. I convert the 27dBm and 3dBm -> 10^2.7-10^0.3.But how can we simply ...
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 ...
787 views

How to calculate power loss between radio and antenna

I have a 5W HT that only kicks out about 1W by the time it hits my antenna (which I understand is the norm). How do I go about calculating power loss in various equipment?
227 views

dBm signal minus dB

I've got a 27dBm signal that I'm going to put through a 6dB attenuator. How do I work out the resultant signal in dBm? I've tried Googling that without any luck.
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 ...
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} +{...
403 views

The right antenna size

I'm preparing for the USA Technician exam and I was reading in the manual that the ideal size for a dipole is following this strange formula: 1/2-lambda. But based on what I read after, it seems it ...
5k views

Conversion from Baud to Bits per Second and then to Bytes per Second

How would I go about converting from Baud to Bits per Second (bps) and then from Bits per Second to Bytes per Second (Bps)?
3k views

How to calculate the peak-to-peak voltage of a sine wave given RMS voltage

How do I calculate the peak-to-peak voltage of a sine wave given RMS voltage?
932 views

How does power received by a dipole relate to electric field intensity?

Let's say there's a transmitter far away, and I'm going to receive the transmitted signal. To keep things simple let's further say the transmitted signal is a pure, unmodulated sine wave. Further, let'...
240 views

Exactly why do some SWR meters give a changing reading depending on the length of coax used to connect to an antenna?

Following is my understanding of some theory and the questions are at the end. Is this right ? ... A standing wave is an AC waveform oscillating at a particular frequency which has a varying ...
1k views

Is transmission wattage calculated using RMS?

I understand (and correct me if I'm wrong) that transmission power follows Ohm's law ($I = \frac{V}{R}$), that is that if I have a 50 Ω antenna that I know is transmitting at 1 W, then the current is: ...
230 views

Would I be able to legally operate this FM transmitter without a license in Canada?

I've been looking into FM transmitters, and I've found one that I think I may use. The transmitter is based off of the KT0803L integrated circuit (http://radio-z.ucoz.lv/kt_0803/KT0803L_V1.3.pdf). The ...
72 views

How to decode a message with unknown bit rate in interstellar signal

I have a question about FSK modulation I'm going to frame in terms of a hypothetical: Imagine that you are transmitting a message to an ET in another solar system. The message is encoded in binary ...