RedcrabX – Electrical Engineering Functions

Reference for the Electrics & Electronics panel  |  Chapter 19 of the MathBox Guide

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Table of Contents

• Overview & Naming Convention
• Basics – Coulomb’s Law, Charge & Energy
• AC Voltage Characteristics – altvolt
• Sine Voltage at Angle – voltang
• Sine Voltage at Time – voltime
• AC Period / Frequency – acperiod
• RMS Square Wave – rmssqr
• RMS Triangular Wave – rmstri
• Ohm’s Law and Power
• Capacitor
• RC Cutoff Frequency – rcfc
• Inductor
• Power Factor, Apparent Power, Reactive Power
• Three-Phase (Symmetrical Star / Wye)
• Wires & Resistors
• RC Series Circuit – rcseries
• RL Series Circuit – rlseries
• Series RLC Resonance – lcrres
• RLC Series Circuit – lcrseries
• RLC Parallel Circuit – lcrparallel
• Parallel RLC Resonance – lcrrespar
• RL Parallel Circuit – rlparallel
• RC Charging Voltage – rccharge
• RC Discharging Voltage – rcdischarge
• RC Component Solver – rcval
• RC Parallel Circuit – rcparallel
• RC Filter Design – rcfilter
• RC Low-Pass Analysis – rclp
• RC High-Pass Analysis – rchp
• RL Low-Pass Analysis – rllp
• RL High-Pass Analysis – rlhp
• RC Integrator – rcint
• RC Differentiator – rcdif
• Unit Display
• Quick-Reference Card

Overview & Naming Convention

The Electrics & Electronics panel provides physics and engineering formulas. Results of direct function calls show their SI unit automatically (e.g. W, V, A, Ω). Assigned variables remain plain numbers.

All functions follow the pattern result_inputs(…):
the part before the underscore is the quantity being calculated, the part after lists the known inputs.

resist_ui(U, I)    →  R = U / I   [Ω]   (resistance from voltage and current)
pow_ir(I, R)    →  P = I² · R  [W]   (power from current and resistance)

Basics – Coulomb’s Law, Charge & Energy

coulomb(1e-6, 1e-6, 0.1)     →  0.8988 N
charge(I=2, t=5)              →  10 C
charge(Q=10, t=5)             →  2 A
charge(Q=10, I=2)             →  5 s
energy(P=100, t=3600)         →  360000 J
energy(E=360000, t=3600)      →  100 W
energy(E=360000, P=100)       →  3600 s

AC Voltage Characteristics – altvolt

Computes all four standard sine-wave voltage values from a single known quantity. Provide one named parameter; the function returns a named result table with all four values – exactly like voltdrop. Results can be assigned to a variable and accessed via dot notation.

Result table returned by the function:

// Direct call – shows all four values as a table:
altvolt(Ueff=230)   →  Ueff = 230 V  |  Us = 325.27 V  |  Uss = 650.54 V  |  Ug = 207.06 V
altvolt(Us=325.27)  →  same table, computed from peak voltage
altvolt(Uss=650.54) →  same table, computed from peak-to-peak voltage
altvolt(Ug=207.06)  →  same table, computed from rectified mean

// Assignment and member access:
a := altvolt(Ueff=230)
a.Us    →  325.27 V
a.Uss   →  650.54 V
a.Ug    →  207.06 V

Sine Voltage at Angle – voltang

Returns the instantaneous voltage of a sinusoidal signal at a given angle φ. The formula is u(φ) = U_eff · √2 · sin(φ).

Formula:

u(φ) = U_eff · √2 · sin(φ)    [V]

voltang(230, 0)    →    0.00 V      // zero crossing
voltang(230, 45)   →  230.00 V      // 45°
voltang(230, 90)   →  325.27 V      // peak  (= Us = Ueff·√2)
voltang(230, 135)  →  230.00 V
voltang(230, 180)  →    0.00 V      // zero crossing
voltang(230, 270)  → -325.27 V      // negative peak

Sine Voltage at Time – voltime

Returns the instantaneous voltage of a sinusoidal signal at a given point in time. The time is specified in milliseconds. Formula: u(t) = U_eff · √2 · sin(2π · f · t ⁄ 1000)

Formula:

u(t) = U_eff · √2 · sin(2π · f · t ⁄ 1000)    [V]

// 230 V / 50 Hz – period T = 20 ms
voltime(230, 50, 0)     →    0.00 V   // zero crossing  (t = 0)
voltime(230, 50, 5)     →  325.27 V   // peak           (t = T/4)
voltime(230, 50, 10)    →    0.00 V   // zero crossing  (t = T/2)
voltime(230, 50, 15)    → -325.27 V   // negative peak  (t = 3T/4)
voltime(230, 50, 20)    →    0.00 V   // full period    (t = T)

// 120 V / 60 Hz – period T ≈ 16.67 ms
voltime(120, 60, 4.167) →  169.71 V   // peak

AC Period / Frequency – acperiod

Converts between period T and frequency f of an AC signal. Supply one named parameter; the other is calculated. Formula: T = 1 / f

acperiod(f=50)    →  0.02 s    // period at 50 Hz
acperiod(f=60)    →  0.0167 s  // period at 60 Hz
acperiod(T=0.02)  →  50 Hz    // frequency for 20 ms period

RMS Square Wave – rmssqr

Returns the RMS (effective) value of a symmetric square wave. For a square wave the amplitude equals the RMS value directly. Formula: U_rms = U

rmssqr(10)   →  10 V   // Us = 10 V square wave → U_rms = 10 V
rmssqr(325)  → 325 V   // compare: sine wave 230 V RMS has Us = 325 V but U_rms_sine = 230 V

RMS Triangular Wave – rmstri

Returns the RMS (effective) value of a symmetric triangular wave. Formula: U_rms = V_s / √3

rmstri(10)   →   5.774 V   // Vs = 10 V triangle → U_rms = 10/√3
rmstri(100)  →  57.74 V   // compare: rmssqr(100) = 100 V, altvolt(Us=100) → 70.71 V (sine)

Ohm’s Law and Power

uri(R=400, I=0.5)    →  200 V    // voltage
uri(U=200, I=0.5)    →  400 Ω   // resistance
uri(U=200, R=400)    →  0.5 A    // current

epow(U=230, I=10)    →  2300 W   // power
epow(P=2300, I=10)   →  230 V    // voltage
epow(P=2300, U=230)  →  10 A     // current

Capacitor

// Named-parameter form  –  supply any two of X (reactance), C (capacitance), f (frequency)
xc(X=8, f=1000)              →  19.894 µF  // capacitance from Xc and f
xc(C=100e-6, f=50)           →  31.831 Ω  // reactance from C and f
xc(X=31.831, C=100e-6)      →  50 Hz      // frequency from Xc and C

// Named-parameter form  –  supply any two of tau (τ), R, C
taurc(R=1000, C=100e-6)      →  0.1 s      // time constant
taurc(tau=0.1, C=100e-6)    →  1000 Ω     // resistance
taurc(tau=0.1, R=1000)       →  100 µF     // capacitance

// rcfc  –  supply any two of R [Ω], C [F], fc [Hz]
rcfc(R=1000, C=100e-9)       →  1591.55 Hz // cutoff frequency
rcfc(fc=1000, C=100e-9)      →  1591.55 Ω  // resistance
rcfc(R=1000, fc=1000)        →  159.15 nF  // capacitance

// rlfc  –  supply any two of R [Ω], L [H], f [Hz]
rlfc(R=1000, L=100e-3)       →  1591.55 Hz // cutoff frequency
rlfc(f=1000, L=100e-3)       →   628.32 Ω  // resistance
rlfc(R=1000, f=1000)         →   159.15 mH // inductance

// Named-parameter form  –  supply any two of Q (charge), C (capacitance), U (voltage)
capq(C=100e-6, U=230)        →  0.023 C    // charge
capq(Q=0.023, U=230)         →  100 µF     // capacitance
capq(Q=0.023, C=100e-6)     →  230 V      // voltage

RC Cutoff Frequency – rcfc

Solves for the missing quantity in the RC cutoff-frequency formula f_c = 1 / (2π R C). Provide any two of R [Ω], C [F], fc [Hz]; the third is computed.

rcfc(R=1000, C=100e-9)       →  1591.55 Hz   // cutoff frequency for 1 kΩ / 100 nF
rcfc(fc=1000, C=100e-9)      →  1591.55 Ω    // required R for fc=1 kHz, C=100 nF
rcfc(R=1000, fc=1000)        →   159.15 nF   // required C for fc=1 kHz, R=1 kΩ

Inductor

induc_el(0.1, 5)           →  1.25 J      // energy at 5 A
xl(f=50, L=0.1)            →  31.42 Ω    // reactance at 50 Hz
xl(Xl=31.42, L=0.1)        →  50 Hz      // frequency
xl(Xl=31.42, f=50)         →  0.1 H      // inductance
taul(L=0.1, R=10)          →  0.01 s     // RL time constant
taul(tau=0.01, R=10)       →  0.1 H      // inductance
taul(tau=0.01, L=0.1)      →  10 Ω       // resistance
rlfc(R=1000, L=100e-3)     →  1591.55 Hz // cutoff frequency
rlfc(f=1000, L=100e-3)     →   628.32 Ω  // resistance
rlfc(R=1000, f=1000)       →   159.15 mH // inductance
luit(L=0.01, I=2, t=0.001) →  20 V       // voltage  (U = L·I/t)
luit(U=20, I=2, t=0.001)   →  0.01 H     // inductance
luit(L=0.01, U=20, t=0.001)→  2 A        // current
luit(L=0.01, U=20, I=2)    →  0.001 s    // time

Power Factor, Apparent Power, Reactive Power

pow_factor(3000, 4000)    →  0.6         // power factor
apparent_pow(3000, 4000)    →  5000 VA     // apparent power
pow_phase(0.8)          →  36.87°      // phase angle

Three-Phase (Symmetrical Star / Wye)

ph3pow(Ul=400, Il=10, cosφ=0.8)    →  5542.6 W   // active power
ph3pow(P=5542.6, Ul=400, cosφ=0.8) →  10 A       // line current
ph3pow(P=5542.6, Il=10, cosφ=0.8)  →  400 V      // line voltage
ph3pow(Ul=400, Il=10, P=5542.6)    →  0.8         // power factor

Wires & Resistors

Wire Resistance – wireres

Solves R = ρ·l / A for any unknown. Provide the material property plus any two of R, l, A; the third is computed.

Material property (first parameter):

• rho – resistivity ρ in Ω·m  (Cu = 1.72×10⁻⁸, Al = 2.82×10⁻⁸, Fe ≈ 1×10⁻⁷)
• sig – conductivity σ in S/m  (Cu ≈ 58×10⁶, Al ≈ 35×10⁶) — converted automatically via ρ = 1/σ

// resistivity form (rho in Ω·m, l in m, A in m²)
wireres(rho=1.72e-8, l=100, A=2.5e-6)   →  0.688 Ω    // 100 m Cu cable, 2.5 mm²
wireres(rho=1.72e-8, l=100, R=0.688)    →  2.5e-6 m²  // required cross-section
wireres(rho=1.72e-8, R=0.688, A=2.5e-6) →  100 m       // wire length

// conductivity form (sig in S/m)
wireres(sig=58e6, l=100, A=2.5e-6)      →  0.690 Ω    // approx Cu
wireres(sig=35e6, l=50, A=16e-6)        →  0.089 Ω    // Al 50 m, 16 mm²

Voltage Drop – voltdrop

Calculates the voltage drop in a two-wire line and returns a named result table with four quantities. The material is specified as resistivity rho (ρ in Ω·m) or conductivity sig (σ in S/m). The power-factor angle φ is in degrees (0° = purely resistive load).

ΔU = 2 × l σ × A × I × cos(φ)

Result table returned by the function:

Typical material values:

voltdrop(rho=1.72e-8, 230, 16, 50, 2.5e-6, 0)
  →  ΔU   8.79 V
     ΔU%  3.82 %
     U_R  221.21 V
     R    0.344 Ω

voltdrop(sig=58e6, 400, 63, 120, 35e-6, 25)
  →  ΔU   11.74 V
     ΔU%  2.94 %
     U_R  388.26 V
     R    0.103 Ω

Assigning the result & accessing individual rows

The result table can be assigned to a variable. Each row is then accessible via dot notation:

// Assign and display the full result table:
vd = voltdrop(rho=1.72e-8, Un=230, I=16, l=50, A=2.5e-6, phi=0)=

// Access individual results afterwards:
vd.dU      →  8.79 V        // voltage drop
vd.dUpct   →  3.82 %        // percentage drop
vd.U_R     →  221.21 V      // remaining voltage at load
vd.R       →  0.344 Ω       // one-way wire resistance

// Use members in further calculations:
efficiency = vd.U_R / 230 * 100   →  96.18 %

Internal Resistance

intres(12.6, 12.0, 5)    →  0.12 Ω      // battery internal resistance
voltser(100, 10, 1000)   →  9000 Ω      // extend 10 V meter to 100 V range
voltser(250, 5, 2000)    →  98000 Ω     // extend 5 V meter to 250 V range
ampshunt(10, 0.1, 50)    →  0.5025 Ω   // extend 100 mA meter to 10 A range
ampshunt(5, 0.05, 100)   →  1.0101 Ω   // extend 50 mA meter to 5 A range

Parallel Resistors

Computes the equivalent resistance of any number of parallel resistors. Accepts a comma-separated list or an array variable. Formula: 1/R = 1/R₁ + 1/R₂ + …

parres(100, 100)        →  50 Ω
parres(10, 20, 30)      →   5.455 Ω
parres(10, 10, 10, 10)  →   2.5 Ω
r := [10, 20, 30]
parres(r)               →   5.455 Ω   // array variable also accepted

Pi Attenuator

Computes the three resistor values of a symmetric Pi (π) attenuator for a given characteristic impedance and attenuation.
Formula: K = 10^dB/20

piatt(50, 6)    →  R1 (shunt)  =  150.93 Ω
                   R2 (series) =   16.61 Ω
                   R3 (shunt)  =  150.93 Ω

piatt(50, 20)   →  R1 = R3 =  61.11 Ω    R2 =  40.91 Ω
piatt(75, 10)   →  R1 = R3 = 141.67 Ω    R2 =  38.39 Ω

a = piatt(50, 6)=    // store and display
a.R2                 // →  16.61 Ω  (series resistor)

T Attenuator

Computes the three resistor values of a symmetric T attenuator for a given characteristic impedance and attenuation.
Formula: K = 10^dB/20

tatt(50, 6)    →  R1 (series) =   16.61 Ω
                  R2 (shunt)  =  150.93 Ω
                  R3 (series) =   16.61 Ω

tatt(50, 20)   →  R1 = R3 =  40.91 Ω    R2 =  61.11 Ω
tatt(75, 10)   →  R1 = R3 =  21.39 Ω    R2 = 105.23 Ω

a = tatt(50, 6)=    // store and display
a.R2                // →  150.93 Ω  (shunt resistor)

RC Series Circuit

Analyses a series RC circuit for a given capacitance, frequency, resistance, and supply voltage. Returns all nine quantities: reactance, impedance, partial voltages, current, and powers.

rcseries(100e-9, 1000, 1000, 230)=
  →  Xc  =  1591.55 Ω
     Z   =  1886.35 Ω
     UR  =   121.92 V
     UC  =   194.05 V
     I   =     0.122 A
     P   =    14.87 W
     Q   =    23.67 var
     S   =    28.08 VA
     φ   =    57.87 °

a = rcseries(100e-9, 1000, 1000, 230)=
a.I       // →  0.122 A
a.phi     // →  57.87 °

RL Series Circuit

Analyses a series RL circuit for a given inductance, resistance, supply voltage, and frequency. Returns all nine quantities: inductive reactance, impedance, partial voltages, current, and powers.

rlseries(0.1, 100, 230, 50)=
  →  XL  =    31.42 Ω
     Z   =   104.82 Ω
     UR  =   219.42 V
     UL  =    68.93 V
     I   =     2.194 A
     P   =   481.44 W
     Q   =   151.26 var
     S   =   504.65 VA
     φ   =    17.44 °

a = rlseries(0.1, 100, 230, 50)=
a.I       // →  2.194 A
a.phi     // →  17.44 °

Series RLC Resonance

Calculates key parameters of a series resonant circuit from inductance, capacitance, resistance and supply voltage.

lcrres(10e-3, 100e-9, 10, 10)=
  →  f0   =   5032.92 Hz
     I0   =      1.00 A
     U0   =    316.23 V
     XL/XC=    316.23 Ω
     Q    =     31.62
     d    =      0.03
     b    =    159.15 Hz
     fo   =   5112.84 Hz
     fu   =   4953.69 Hz
     Ifg  =      0.71 A
     Zfg  =     14.14 Ω

a = lcrres(10e-3, 100e-9, 10, 10)=
a.f0   // resonance frequency
a.Q    // quality factor

RLC Series Circuit

Analyses an RLC series circuit (L, C, and R in series) for given frequency and supply voltage. Returns reactances, voltages, current, and power components.

lcrseries(10e-3, 100e-9, 50, 1000, 230)=
  →  XL  =    62.83 Ω
     XC  =  1591.55 Ω
     Z   =  1529.54 Ω
     UL  =     9.45 V
     UC  =   239.40 V
     UR  =     7.52 V
     I   =     0.150 A
     P   =     1.13 W
     QL  =     1.42 var
     QC  =    35.88 var
     S   =    34.60 VA
     φ   =   -88.13 °

a = lcrseries(10e-3, 100e-9, 50, 1000, 230)=
a.I    // total current
a.UL   // inductor voltage

RLC Parallel Circuit

Analyses an RLC parallel circuit (L, C, and R in parallel) for given frequency and supply voltage. Returns reactances, branch currents, total current, and power components.

lcrparallel(10e-3, 100e-9, 1000, 1000, 230)=
  →  XL  =    62.83 Ω
     XC  =  1591.55 Ω
     Z   =    64.90 Ω
     IL  =     3.66 A
     IC  =     0.14 A
     IR  =     0.23 A
     I   =     3.54 A
     P   =    52.90 W
     QL  =   841.87 var
     QC  =    33.22 var
     S   =   815.32 VA
     φ   =   -86.28 °

a = lcrparallel(10e-3, 100e-9, 1000, 1000, 230)=
a.I    // total current
a.IR   // resistor branch current

Parallel RLC Resonance

Calculates key parameters of a parallel resonant circuit (L, C, R in parallel) from inductance, capacitance, resistance and supply voltage.

lcrrespar(10e-3, 100e-9, 1000, 10)=
  →  f0    =   5032.92 Hz
     I0    =      0.010 A
     IL    =      0.032 A
     IC    =      0.032 A
     XL/XC =    316.23 Ω
     Q     =      3.16
     d     =      0.32
     b     =   1591.55 Hz
     fo    =   5828.69 Hz
     fu    =   4237.14 Hz

a = lcrrespar(10e-3, 100e-9, 1000, 10)=
a.f0  // resonance frequency
a.IL  // inductor branch current

RL Parallel Circuit

Analyses a parallel RL circuit for a given inductance, resistance, supply voltage, and frequency. Returns all nine quantities: inductive reactance, equivalent impedance, branch currents, total current, and powers.

rlparallel(0.1, 100, 230, 50)=
  →  XL  =    31.42 Ω
     Z   =    29.99 Ω
     IR  =     2.300 A
     IL  =     7.321 A
     I   =     7.674 A
     P   =   529.00 W
     Q   =  1683.74 var
     S   =  1765.10 VA
     φ   =    72.57 °

a = rlparallel(0.1, 100, 230, 50)=
a.I       // →  7.674 A
a.phi     // →  72.57 °

RC Charging Voltage

Calculates the capacitor voltage during charging at a given time t. The supply voltage U is applied via resistor R to capacitor C.

rccharge(1000, 100e-9, 12, 500e-6)
  →  Uc  =  10.44 V    // τ = 100 μs, 5τ = 500 μs → fully charged

rccharge(10e3, 10e-6, 5, 50e-3)
  →  Uc  =   3.16 V    // t = 0.5τ

RC Discharging Voltage

Calculates the capacitor voltage during discharging at a given time t. The initially charged capacitor C discharges through resistor R.

rcdischarge(1000, 100e-9, 12, 500e-6)
  →  Uc  =   1.56 V    // t = 5τ → nearly discharged

rcdischarge(10e3, 10e-6, 5, 50e-3)
  →  Uc  =   3.03 V    // t = 0.5τ

RC Component Solver

Solves the missing RC component (R or C) from a known charging voltage at a given time. Based on the rearrangement of the charging formula: τ = −t / ln(1 − U_lade / U_ein)

// Find R: capacitor 100 nF must reach 10 V from 12 V in 500 µs
rcval(U=12, Ul=10, t=500e-6, C=100e-9)
  →  2763.51 Ω

// Find C: resistor 1 kΩ, same conditions
rcval(U=12, Ul=10, t=500e-6, R=1000)
  →  276.35 nF

// Verify with rccharge
rccharge(2763.51, 100e-9, 12, 500e-6)
  →  10.00 V

RC Parallel Circuit

Analyses a parallel RC circuit for a given capacitance, frequency, resistance, and supply voltage. Returns all nine quantities: reactance, impedance, branch currents, total current, phase angle, and powers.

rcparallel(100e-9, 1000, 1000, 230)=
  →  Xc  =  1591.55 Ω
     Z   =   847.00 Ω
     IR  =     0.230 A
     IC  =     0.145 A
     I   =     0.271 A
     φ   =    32.14 °
     P   =    52.90 W
     Q   =    33.35 var
     S   =    62.44 VA

a = rcparallel(100e-9, 1000, 1000, 230)=
a.I       // →  0.271 A
a.phi     // →  32.14 °

RC Filter Component Design

Calculates the resistor and capacitor values needed to build an RC low-pass (or high-pass) filter with a specified total impedance Z and −3 dB cutoff frequency f_c. At the cutoff frequency the capacitive reactance equals the resistance (Xc = R), so the total impedance is Z = R √2. Given Z the component values follow as R = Z / √2 and C = 1 / (2π f_c R).

// RC low-pass filter: Z=1 kΩ, fc=1 kHz  →  R=707.1 Ω, C=224.9 nF
rcfilter(1000, 1000)=
  →  R   =   707.11 Ω
     C   =   224.94 nF
     τ   =   159.15 µs
     Xc  =   707.11 Ω    // = R ✓

// Audio low-pass at 20 kHz, Z=600 Ω
rcfilter(600, 20000)=
  →  R   =   424.26 Ω
     C   =    18.76 nF
     τ   =     7.96 µs
     Xc  =   424.26 Ω    // = R ✓

a = rcfilter(1000, 1000)=
a.C       // → 224.94 nF
a.tau     // → 159.15 µs

RC Low-Pass Filter Analysis

Analyses a series RC low-pass circuit (resistor in series, capacitor to ground / output across C) at a given operating frequency f and input voltage U. Returns all key electrical properties of the filter at that frequency.

// RC low-pass: R=1 kΩ, C=100 nF, f=1 kHz, U=10 V
rclp(1000, 100e-9, 1000, 10)=
  →  Xc  =  1591.55 Ω
     U2  =     8.47 V
     dB  =    -1.44 dB
     φ   =   -32.14 °
     f0  =  1591.55 Hz
     Z   =  1880.72 Ω
     UR  =     5.32 V
     I   =     5.32 mA
     τ   =   100.00 µs

// Member access
a = rclp(1000, 100e-9, 1000, 10)=
a.U2    // → output voltage
a.phi   // → phase angle in degrees
a.f0    // → cutoff frequency

RC High-Pass Filter Analysis

Analyses a series RC high-pass circuit (capacitor in series, output measured across R) at a given operating frequency f and input voltage U. At the cutoff frequency the output is −3 dB and the phase lead is +45°.

// RC high-pass: R=1 kΩ, C=100 nF, f=1 kHz, U=10 V
rchp(1000, 100e-9, 1000, 10)=
  →  Xc  =  1591.55 Ω
     U2  =     5.32 V
     dB  =    -5.45 dB
     φ   =   +57.86 °
     f0  =  1591.55 Hz
     Z   =  1880.72 Ω
     UC  =     8.47 V
     I   =     5.32 mA
     τ   =   100.00 µs

// Member access
a = rchp(1000, 100e-9, 1000, 10)=
a.U2    // → output voltage
a.phi   // → phase lead in degrees
a.f0    // → cutoff frequency

RL Low-Pass Filter Analysis

Analyses a series RL low-pass circuit (resistor and inductor in series, output measured across R) at a given operating frequency f and input voltage U. Returns the requested key quantities: inductive reactance, output voltage, attenuation, and phase shift.

// RL low-pass: R=1 kΩ, L=100 mH, f=1 kHz, U=10 V
rllp(1000, 100e-3, 1000, 10)=
  →  XL  =   628.32 Ω
     U2  =     8.47 V
     dB  =    -1.44 dB
     φ   =   -32.14 °

// Member access
a = rllp(1000, 100e-3, 1000, 10)=
a.U2    // → output voltage
a.phi   // → phase lag in degrees

RL High-Pass Filter Analysis

Analyses a series RL high-pass circuit (resistor and inductor in series, output measured across L) at a given operating frequency f and input voltage U. Returns the requested key quantities: inductive reactance, output voltage, attenuation, and phase shift.

// RL high-pass: R=1 kΩ, L=100 mH, f=1 kHz, U=10 V
rlhp(1000, 100e-3, 1000, 10)=
  →  XL  =   628.32 Ω
     U2  =     5.32 V
     dB  =    -5.48 dB
     φ   =   +57.86 °

// Member access
a = rlhp(1000, 100e-3, 1000, 10)=
a.U2    // → output voltage
a.phi   // → phase lead in degrees

RC Integrator (Integrierglied)

Calculates the component values for a fully integrated RC integrator circuit using the 5τ rule: for optimal ramp formation the input pulse width t₁ must equal 5τ. For a symmetric square wave the full period is T = 2 t₁ = 10τ, giving f = 1 / (10 R C). Supply any two of R, C, f, T to compute all other quantities.

// rcint  –  supply any two of R [Ω], C [F], f [Hz], T [s]
rcint(R=1000, C=100e-9)=
  →  R   =   1000.00 Ω
     C   =    100.00 nF
     τ   =    100.00 µs    // = R · C
     t1  =    500.00 µs    // = 5τ  (optimal pulse width)
     T   =      1.00 ms    // = 10τ  (full period)
     f   =   1000.00 Hz    // = 1/(10τ)

rcint(R=1000, f=500)=
  →  C   =    200.00 nF    // computed
     τ   =    200.00 µs
     t1  =      1.00 ms
     T   =      2.00 ms

rcint(C=47e-9, T=2e-3)=
  →  R   =   4255.32 Ω    // computed
     τ   =    200.00 µs
     t1  =      1.00 ms
     f   =    500.00 Hz

// Member access
a = rcint(R=1000, C=100e-9)=
a.tau   // → 100.00 µs
a.t1    // → 500.00 µs
a.T     // →   1.00 ms
a.f     // → 1000.00 Hz

RC Differentiator (Differenzierglied)

Calculates component values for a properly differentiated RC circuit using the 5τ rule: for clean spike output the input pulse width t₁ must equal 5τ (τ ≪ T). For a symmetric square wave the full period is T = 2 t₁ = 10τ, giving f = 1 / (10 R C). Circuit topology: capacitor in series, output taken across R (high-pass behaviour). Supply any two of R, C, f, T to compute all other quantities.

// rcdif  –  supply any two of R [Ω], C [F], f [Hz], T [s]
rcdif(R=1000, C=100e-9)=
  →  R   =   1000.00 Ω
     C   =    100.00 nF
     τ   =    100.00 µs    // = R · C
     t1  =    500.00 µs    // = 5τ  (half-period pulse width)
     T   =      1.00 ms    // = 10τ  (full period)
     f   =   1000.00 Hz    // = 1/(10τ)

rcdif(R=1000, f=500)=
  →  C   =    200.00 nF    // computed
     τ   =    200.00 µs
     t1  =      1.00 ms
     T   =      2.00 ms

rcdif(C=47e-9, T=2e-3)=
  →  R   =   4255.32 Ω    // computed
     τ   =    200.00 µs
     t1  =      1.00 ms
     f   =    500.00 Hz

// Member access
a = rcdif(R=1000, C=100e-9)=
a.tau   // → 100.00 µs
a.t1    // → 500.00 µs
a.T     // →   1.00 ms
a.f     // → 1000.00 Hz

Temperature Drift of Resistance

Models how conductor resistance changes with temperature using the named-parameter solver resdrift. α is the temperature coefficient of resistance (1/K); for copper α ≈ 0.00393 K⁻¹. Rk is the reference resistance at 20 °C. Provide alpha, Rk, and one of dT or Rw; the missing quantity is computed.

Formula: ΔR = α × ΔT × R_k

resdrift(alpha=0.00393, Rk=100, dT=80)     →  131.44 Ω   // Cu wire, 80 K rise
resdrift(alpha=0.00393, Rk=100, Rw=131.44) →  80 K        // reverse: find temperature

dB Converter – dbcon

Named-parameter solver for decibel conversions. The mode (power or voltage) is detected automatically from the parameter names. Provide any two of the three parameters; the missing one is computed.

// Power mode  (factor 10)
dbcon(P1=2, P2=1)        →  3.01 dB    // level from two powers
dbcon(P1=2, db=3.01)     →  1 W        // reference power P2
dbcon(P2=1, db=3.01)     →  2 W        // input power P1

// Voltage mode  (factor 20)
dbcon(U1=2, U2=1)        →  6.02 dB   // level from two voltages
dbcon(U1=2, db=6.02)     →  1 V        // reference voltage U2
dbcon(U2=1, db=6.02)     →  2 V        // input voltage U1

Unit Display

When a result is produced by a direct electrical function call (not an assignment), MathBox appends the SI unit automatically:

pow_ui(230, 10)          →  2300 W
resist_ui(230, 10)          →  23 Ω
P := pow_ui(230, 10)     →  (no unit shown; plain variable assignment)

Quick-Reference Card

── Basics ───────────────────────────────────────────────
coulomb                            Coulomb force                [N]
charge(Q=…,I=…)  charge(Q=…,t=…)  charge(I=…,t=…)   charge solver  [C/A/s]
energy(E=…,P=…)  energy(E=…,t=…)  energy(P=…,t=…)   energy solver  [J/W/s]

── EC Electrical ────────────────────────────────────────
altvolt(Ueff=…)  altvolt(Us=…)  altvolt(Uss=…)  altvolt(Ug=…)
  → named table: .Ueff [V]  .Us [V]  .Uss [V]  .Ug [V]
  Us = Ueff·√2  |  Uss = 2·Us  |  Ug = (2/π)·Us
voltang(Ueff, φ)          u(φ) = Ueff·√2·sin(φ)              [V]  – sine voltage at angle (deg/rad toolbar)
voltime(Ueff, f, t_ms)    u(t) = Ueff·√2·sin(2π·f·t/1000)  [V]  – sine voltage at time t [ms]

── Ohm / Power ──────────────────────────────────────────
uri(R=…,I=…)  uri(U=…,I=…)  uri(U=…,R=…)   named-param Ohm solver   [V/Ω/A]
epow(U=…,I=…)  epow(P=…,I=…)  epow(P=…,U=…)  named-param power solver  [W/V/A]

── Capacitor ────────────────────────────────────────────
xc(X=…,C=…)  xc(C=…,f=…)  xc(X=…,f=…)            named-param reactance solver  [Ω/F/Hz]
taurc(tau=…,R=…)  taurc(tau=…,C=…)  taurc(R=…,C=…)  named-param RC time constant  [s/Ω/F]
rcfc(R=…,C=…)  rcfc(fc=…,C=…)  rcfc(R=…,fc=…)      named-param RC cutoff freq    [Hz/Ω/F]
capq(Q=…,C=…)  capq(Q=…,U=…)  capq(C=…,U=…)        named-param charge solver     [C/F/V]

── Inductor ─────────────────────────────────────────────
induc_el               energy stored in inductor                    [J]
luit                   inductor law U=L·I/t, solve for any one param [V/H/A/s]
rlfc(R=…,L=…)  rlfc(f=…,L=…)  rlfc(R=…,f=…)      named-param RL cutoff freq    [Hz/Ω/H]
lcres(L=…,C=…)  lcres(f=…,C=…)  lcres(L=…,f=…)      named-param LC resonance freq  [Hz/H/F]
xl(f=…,L=…)  xl(Xl=…,L=…)  xl(Xl=…,f=…)  named-param reactance solver  [Ω/H/Hz]
taul(L=…,R=…)  taul(tau=…,R=…)  taul(tau=…,L=…)  named-param RL τ solver  [s/H/Ω]

── AC Signals ──────────────────────────────────────────
acperiod(f=…)  acperiod(T=…)   period / frequency converter          [s/Hz]
rmssqr(Us)                       RMS of square wave  U_rms = Us        [V]
rmstri(Vs)                       RMS of triangular wave  U_rms = Vs/√3  [V]

── Power Factor ─────────────────────────────────────────
pow_factor  apparent_pow  reactive_pow  active_pow  pow_phase                             [–/VA/var/W/°]

── Three-Phase ──────────────────────────────────────────
phase3_s3  ph3uphase  ph3uline
ph3pow(Ul=…,Il=…,cosφ=…)  three-phase solver (named params, any 3 of Ul/Il/cosφ/P)  [W/A/V/–]

── Wires & Resistors ────────────────────────────────────
wireres(rho=…,l=…,A=…) wireres(rho=…,l=…,R=…) wireres(rho=…,R=…,A=…)  named-param wire resistance  [Ω/m²/m]
wireres(sig=…,l=…,A=…)  (sig = conductivity in S/m instead of rho)
voltdrop(rho=…|sig=…, Un, I, l, A, phi)  voltage drop table  [V / % / V / Ω]
  members: vd.dU  vd.dUpct  vd.U_R  vd.R
intres(Uq, U2, I)                internal resistance                    [Ω]
voltser(Unew, Um, Rm)            voltmeter series resistor  Rs = Rm·(Unew/Um−1)  [Ω]
ampshunt(Inew, Im, Rm)           ammeter shunt resistor     Rs = Rm·Im/(Inew−Im)  [Ω]
parres(R1, R2, ...)              parallel resistors  1/R = Σ 1/Ri       [Ω]
piatt(Z, dB)                     Pi attenuator → R1(shunt) R2(series) R3(shunt)  [Ω]
tatt(Z, dB)                      T attenuator  → R1(series) R2(shunt) R3(series)  [Ω]
rcseries(C, f, R, U)             RC series     → Xc, Z, UR, UC, I, P, Q, S, φ
rlseries(L, R, U, f)             RL series     → XL, Z, UR, UL, I, P, Q, S, φ
lcrres(L, C, R, U)               series RLC resonance → f0, I0, U0, XL/XC, Q, d, b, fo, fu, Ifg, Zfg
lcrseries(L, C, R, f, U)         RLC series   → XL, XC, Z, UL, UC, UR, I, P, QL, QC, S, φ
lcrparallel(L, C, R, f, U)       RLC parallel → XL, XC, Z, IL, IC, IR, I, P, QL, QC, S, φ
lcrrespar(L, C, R, U)           parallel RLC resonance → f0, I0, IL, IC, XL/XC, Q, d, b, fo, fu
rlparallel(L, R, U, f)           RL parallel   → XL, Z, IR, IL, I, P, Q, S, φ
rcparallel(C, f, R, U)           RC parallel   → Xc, Z, IR, IC, I, φ, P, Q, S
rcfilter(Z, fc)                  RC filter design → R [Ω], C [F], τ [s], Xc [Ω]
rllp(R, L, f, U)                 RL low-pass   → XL, U2, dB, φ
rlhp(R, L, f, U)                 RL high-pass  → XL, U2, dB, φ
resdrift(alpha=…,Rk=…,dT=…)     → Rw [Ω]   resistance temperature drift
resdrift(alpha=…,Rk=…,Rw=…)     → dT [K]

── dB Converter ─────────────────────────────────────────
dbcon(P1=…,P2=…)  dbcon(P1=…,db=…)  dbcon(P2=…,db=…)  power dB solver   [dB/W/W]
dbcon(U1=…,U2=…)  dbcon(U1=…,db=…)  dbcon(U2=…,db=…)  voltage dB solver [dB/V/V]