# Tag Info

## Hot answers tagged math

Accepted

### Is free space path loss dependent on frequency?

Mathematically yes, the value of that equation increases with frequency. However, that's not to say there's some physical mechanism for frequency-dependent attenuation in free space. Rather, the ...
• 49.8k
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### Why EME with 100W and a single Yagi-Uda antenna is possible?

You didn't include antenna gain at all. That number for the path loss is a starting point assuming zero gain (isotropic antennas) on both ends. This isn't a realistic situation, because of course the ...
• 8,740
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### Conversion from Baud to Bits per Second and then to Bytes per Second

Baud is another name for symbols per second (a unit of symbol rate), so you can't convert between it and the others (which are units of bit rate) without knowing how many symbols are in use. A symbol ...
• 22.7k
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### How can I calculate the effects of an LNA, antenna gain, etc. on noise performance?

Try the Friis noise formula: $$F_{eq} = F_1 + {F_2-1 \over G_1} + {F_3-1 \over G_1 G_2} + \cdots \tag 1$$ $F_n$ is the noise factor of the n-th component, and likewise $G_n$ is the gain. The noise ...
• 49.8k

### How does IQ modulation work (intuitively)?

I think it's more intuitive if you unlearn some things first. Oscillation is not: $$\cos(\omega t)$$ where $\omega$ is the angular frequency in radians per second, and $t$ is time. Rather, ...
• 49.8k
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### Adding and subtracting dB/dBm/dBi values

A value given in "dB" is a dimensionless ratio. 10dB is a ratio of 10:1, -10dB is a ratio of 1:10, 3dB is a ratio of approximately 2:1, etc. dBi is dimensionless; it represents decibels ...
• 8,740
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### What is dB(μV/m), and what are its applications?

TL;DR: $\frac{V}{m}$ and $\text{dB}(\mu V/m)$ are units for the field strength of an electric field. For a practical application skip to the end! Derivation of the field strength A point charge $q_1$ ...
• 399
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### How does FM encode BOTH amplitude and frequencies of full audio signal spectrum?

Whatever modulation we use, there's a baseband signal we wish to transmit (music, voice recording, whatever), which somehow modulates a carrier to produce the output signal. Your question suggests ...
• 49.8k
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### Decibel subtraction in dBm and dB

I convert the 27dBm and 3dBm -> 10^2.7-10^0.3. But how can we simply subtract the two dBm If you convert to exponential form then you must simultaneously replace ...
• 22.7k
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### dBm signal minus dB

Decibels are all "ratios" at their core. A unitless dB is a simply a ratio of one number to another, perhaps input power relative to output power. We can also use decibels for absolute values, by ...
• 5,955
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### FT8 callsign/maidenhead compression encoding

You can find the code in packjt77.f90. Callsign encoding (for "standard" callsigns that don't require hashing) is in function pack28. A quick summary: ...
• 8,740
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### Why is the neper a useful unit for transmission line calculations?

A neper, just like a decibel, is a logarithmic expression of ratios. The decibel uses the base-10, or decadic, logarithm while the neper uses the natural, or Euler constant, logarithm. The decibel is ...
• 18.1k
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### How does power received by a dipole relate to electric field intensity?

There are a lot of ways to approach this problem, but here's one: we can calculate the power density of that field, and determine the area from which the antenna captures power, and multiply them ...
• 49.8k
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### Exactly why do some SWR meters give a changing reading depending on the length of coax used to connect to an antenna?

The SWR is related to the reflection coefficient $\Gamma$: $$\Gamma = {Z_L - Z_0 \over Z_L + Z_0 }$$ $$\text{VSWR} = {1+|\Gamma| \over 1 - |\Gamma|}$$ where: $Z_0$ is the feedline impedance, ...
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### dBm signal minus dB

Think about it this way. 27 dBm means 27dB above a milliwatt. Take 6dB away. Now you have something that's 21 dB above a milliwatt. Or, 21 dBm.
• 1,023

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

Look closer at the diagram. At the two wires coming from the source, the voltage is NOT always zero. The only way for the voltage at the center point to be zero is for the two source wires to occupy ...
• 1,646

### The right antenna size

The classic dipole is a half-wave antenna. This means that the total length of the antenna is lambda/2. So writing it as 1/2-lambda is OK from an English language point of view, but not IMO as a ...
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### Is free space path loss dependent on frequency?

I'd like to offer a parallel and simplified explanation to W8II's correct answer above, for the mathematically-challenged VHF+ enthusiasts among us. :-) As was mentioned in recent threads here, ...
• 7,485
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### Why is antenna aperture a function of wavelength?

This is a topic that troubles most students and even finds it way into many technical papers and textbooks in the form of incorrect assertions and conclusions. While you will find some reasonable ...
• 18.1k
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### SWR Measured at the Transmitter versus SWR at the Antenna

Given the matched loss of the feedline and the SWR at the transmitter, we can calculate the SWR at the antenna in three simple steps. First convert the SWR at the transmitter to the corresponding ...
• 18.1k

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

I generally understand that AM side bands occupy sufficiently wide band width to recreate the spectrum of the modulating audio signal (while varying amplitude at each frequency in the spectrum of the ...
• 22.7k

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

An FSK signal which is the same symbol repeated is an unmodulated carrier, and like an unmodulated carrier, it contains no information. Making some assumptions about the bit shaping filter it might be ...
• 49.8k

### The right antenna size

If you make a dipole exactly a half-wavelength long, then it will be too long and out of resonance. The formula for determining the length of a half-wavelength dipole in feet is 468÷frequency in MHz. ...
• 7,485

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

The simple answer is that the graphic is not accurate. There is an RMS voltage present at the center feed point of the dipole that follows Ohm's law relative to the feed point impedance. Most likely, ...
• 18.1k

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

Can someone tell me EXACTLY how the presence of current on the outside of the coax changes the VSWR reading ? When RF current is flowing on the outside of a coaxial cable, the exterior shield has ...
• 18.1k

### How does IQ modulation work (intuitively)?

I believe a good point of view is the concept of orthogonality. This is clear under everybody's eyes when seen in physical space, take for instance a 2-dimension space, a plane. In the example above ...
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### The right antenna size

There are already a couple of nice answers to your question. I thought I would add a little more context - no need to vote for this as it is tangential to the question. A 1/2 wavelength (1/2 $\lambda$...
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### Calculating Antenna Length on the FCC Exam vs. in Reality

Thanks for the posting everyone! For licence test I took this approach after reading everyone's post & searching though all the technical details you posted. Convert Frequency to wavelength in ...