# Questions tagged [math]

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

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### 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{...
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 ...
298 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.
273 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 ? ...
281 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 ...
407 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 ...
73 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 ...
79 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 ...
221 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 ...
74 views

634 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 ...
236 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 ...
996 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'...
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 ...
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)?
76 views

### Getting the wrong answer from percentage power/transmit power calculation

I have the following example taken from the "ARRL General Class Manual", 7th Ed, 4-4. Here's a practical application. Suppose you are using an antenna feed line that has a signal loss of 1dB. You ...
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: ...
7k 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 ...
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?
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 ...