# Tag Info

## Hot answers tagged math

21

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 frequency term is in the equation due to the assumption of unity gain antennas at each end. A larger antenna is required to get the same gain at a lower frequency. ...

18

The $492/f$ formula is for an ideal antenna in free space, the $468/f$ is an estimate for real antennas at a reasonable height over ground. The $492/f$ formula is a conversion from metric units to English units for the fundamental frequency and wavelength ($\lambda$) formula. $c = 3\times 10^8_{m/s}$ (the velocity of light) and $f =$ frequency -- \begin{...

15

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 vast majority of the signal from an isotropic antenna doesn't reach the moon at all, but it's conventional for calculating link budgets. A 9-element Yagi has a ...

12

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 is the smallest unit of a digital modulation. For example, suppose we're doing on-off keying (also known as CW): the signal can be either present or absent, so ...

11

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 factor $F$ is the linear ratio form of the noise figure which is given in decibels. For example, the first component may be an LNA, the second component a ...

10

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, oscillation is: $$e^{i \omega t}$$ By Euler's formula this can be expanded to: $$\cos(\omega t) + i \sin(\omega t)$$ If you plot this function on the complex plane, ...

9

The diagram is a polar plot where 0 degrees (the 0 on the right-hand edge) corresponds to the front of the antenna and 180 degrees corresponds to the back. Within the diagram, a logarithmic scale is utilized to represent radiation strength. This is in addition to the fact that the Decibel is a logarithmic unit. (The diagram really should explicitly list its ...

8

Electrical wave propagation in wire is about 95% to 97% the speed of light. Since wavelength is most commonly used for building antennas, which involve conducting the wave from air into the wire and vice versa, the calculation is adjusted assuming the slower propagation in an unshielded conductor. However, this 3% to 5% discrepancy is small enough at ...

8

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 you are primarily concerned about how the frequency domain representation of the baseband translates to the frequency domain of the output. This is a valid thing ...

8

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 subtraction with division (or addition with multiplication), so you have $10^{2.7} / 10^{0.3}$ instead of $10^{2.7} - 10^{0.3}$. Then you will see that you get the same result: $$2.7 - 0.3 = 2.4$$ ...

8

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 fixing the denominator to a standard reference — e.g. one milliwatt in dBm. But the most convenient thing about decibels is that, although they are ratios, because ...

8

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: Adjust a few strange prefixes that don't follow the usual arrangement of letters and numbers. Swaziland 3DA0* will be encoded as if it was 3D0* instead, and Guinea 3XA1A will be encoded as if it was ...

7

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 strictly defined as the ratio of two powers. $$dB=10\log_{10}\left(\frac{P_1}{P_2}\right) \tag 1$$ While it is common to see a decibel formula based on ...

7

The short answer: $$\frac{V_{p-p}}{V_{rms}} = 2\sqrt{2}$$ The long answer, or how to derive the above: As noted on the Wikipedia page for root mean square, the RMS of a sine wave is equal to its amplitude divided by the square root of two. (You can also derive this by doing the integral over a sine wave yourself.) \begin{...

7

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 together. Calculating the power density If we know the electric field to be 1 mV/m, and the transmitting antenna is distant, then the magnetic field must be ...

7

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, usually 50 ohms, and $Z_L$ is the load (nominally, the antenna) impedance. The reflection coefficient is a complex number and thus takes into account the phase ...

7

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.

7

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 relative to an isotropic radiator. Values given in "dBm", "dBW", "dBV", etc. are dimensioned values, given as decibels relative to ...

6

Let's imagine that there are two antennas, entirely in free space. There is no Earth or any other object near enough to affect propagation. Let's also assume that these antennas are far enough apart that the antennas interact only by their far fields. To start, let's assume that both antennas are isotropic, meaning that they radiate equally in each ...

6

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 $q_1$ generates a field strength* of $E = \frac{1}{4\pi\varepsilon_0}{q_1\over r^2}$ at a distance of $r$. This is derived from Coulomb's law that is $F=\frac{1}{... 6 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 the same point which is impossible. Think about the voltage as an electric field which is indeed zero at the point halfway between the two wires. 5 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 magnitude of the reflection coefficient (Gamma), or MRC for short within the context of this answer. The MRC is the magnitude of the complex ratio of the reflected ... 5 For someone who knows how to convert between inches, feet, and meters, it's really quite simple. You only really need to know one formula to do it all, and that formula is$300=f\times wavelength$. If you find the wavelength for the given frequency, then just find the type of antenna (quarter-wave), take the appropriate fraction of the wavelength, and ... 5 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, effective aperture is a measure of the power captured by an antenna. Effective aperture can be expressed as a function of the antenna gain and the wavelength. Now, ... 5 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 rigorous mathematical formula. For a half-wave dipole, each side of the feedpoint is one-half of that or a quarter-wave. 4 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 references to thermodynamic equivalencies in some texts, it seems the genesis of the isotropic effective aperture equation has been rarely published. The answer to ... 4 Legend$c$= velocity of propogation = speed of light (299,792,458 meters/second)$f$= frequency$\lambda $= wavelength Formulas The basic formula for calculating wavelength is: $$\lambda = \frac{c}{f}$$ To make the math simpler, frequency ($f$) is expressed in megahertz (MHz) and the velocity of propogation in free space ($...

4

There are a few possibilities. First of all, in larger assemblies (mostly important in repeater design) each component will have a parameter called insertion loss. This is the loss, in dB, through that componenet - the loss caused by inserting that component in your feed line. Filters have insertion loss, as do duplexers, and even inline wattmeters and ...

4

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 sound wave)--so the spectrum of a side band should look basically like the spectrum of the underlying modulating audio wave. Is this understanding wrong? This ...

4

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 possible to make a reasonable estimate of the symbol rate judging by the growth and decay of the envelope at the start and end of the transmission, but it's an ...

Only top voted, non community-wiki answers of a minimum length are eligible