parallel(Z1, Z2, …) MathMath’s own
One over the sum of reciprocals: resistors or impedances in parallel, or capacitors in series.
Takes any number of values, or vectors and matrices of them, all in the same units. A short (0) across any branch makes the whole combination 0.
Units
The result is in the values' units, so parallel(1·kΩ, 2·kΩ) is in ohms.
Refused
- Values in different units.
- Branches that cancel, as j·10 Ω beside −j·10 Ω, whose combination is infinite.
parallel(1⋅kΩ,2⋅kΩ)=666.667 Ω
parallel(100⋅Ω,100⋅Ω,50⋅Ω)=25 Ω
phasor(r, θ) MathMath’s own
The complex number of magnitude r at angle θ: r·(cos θ + j·sin θ).
θ is in radians, so 30·deg works. r and θ can be vectors of the same size, or one a vector and the other a number.
To show a complex result as magnitude∠angle, select it and choose Format → Complex results as magnitude∠angle.
Units
r can carry units, as 10·V; θ can't, beyond radians and degrees.
Refused
- An angle with units other than radians or degrees.
- A complex magnitude or angle.
V≔phasor(10⋅V,30⋅deg)
V=8.66+5i V
∣V∣=10 V
powerToDb(ratio) MathMath’s own
A power ratio in decibels: 10·log(ratio).
Element by element for a vector or matrix. For a voltage or current ratio use ampToDb; dbToPower goes back.
Units
The ratio has no units: divide by the reference power first.
Refused
- A negative ratio, or 0, whose decibels are minus infinity.
powerToDb(2)=3.01
powerToDb(50⋅mW5⋅W)=20
ampToDb(ratio) MathMath’s own
An amplitude ratio in decibels: 20·log|ratio|, for voltages, currents and the gain of a transfer function.
A complex ratio counts by its magnitude, so a transfer function's value gives its gain directly. Element by element for a vector or matrix. dbToAmp goes back.
Units
The ratio has no units: divide by the reference first.
Refused
- 0, whose decibels are minus infinity.
ampToDb(0.5)=−6.021
ampToDb(1+1i1)=−3.01
dbToPower(dB) MathMath’s own
The power ratio of a number of decibels: 10^(dB/10).
dbToPower(−3)=0.501
dbToPower(20)=100
dbToAmp(dB) MathMath’s own
The amplitude ratio of a number of decibels: 10^(dB/20).
dbToAmp(20)=10
dbToAmp(−6)=0.501
wattsToDbm(P) MathMath’s own
A power in dBm: decibels above one milliwatt.
Units
P is a power, in W, mW or any other power unit.
Refused
- Something that isn't a power.
- A negative power, or 0.
wattsToDbm(25⋅mW)=13.979
wattsToDbm(1⋅W)=30
dbmToWatts(dBm) MathMath’s own
The power of a number of dBm, in watts.
dbmToWatts(−10)=1×10−4 W
dbmToWatts(30)=1 W
standardValue(x, series) MathMath’s own
The nearest standard part value in an E series: E3, E6, E12, E24, E48, E96 or E192.
Nearest by ratio, as tolerances are, so 4.8 goes to 4.7 in E12. series is 3, 6, 12, 24, 48, 96 or 192. Element by element for a vector or matrix.
Units
The result is in x's units.
Refused
- A series that isn't one of those.
standardValue(4.8⋅μF,12)=4.7×10−6 F
standardValue(5100⋅Ω,96)=5.11×103 Ω