19bb969e-c5a9-4e54-87db-91d9cd2747b4 7 4 5 false false 0 decimal

&[DATE] &[TIME] - &[FILENAME]

RMS

Peak, frequency and period

Xo 40 V * :

ω 3 Hz * :

To 2 π * ω / : 2.0944 s *

Discretize with 500 points over 6 periods

T 6 To * 500 / 0500 range * :

a b Dot To UoM To / a b Conjugate * t 0 To int * :

Distance between two periodic functions
and Eucliedean Norme of a function

a N a a Dot sqrt :

Sinusoid

t x Xo ω t * sin * :

Integral, time domain, freq domain
and theoric RMS values

X.rms t s * x N : X T x vectorize eval : X.Trms X norme X length sqrt / : X.F X fft : X.Frms X.F norme X.F length / : 51 line

T X augment X.rms 2 1 sys

X.rms 28.2843 V *

X.Trms 28.256 V *

X.Frms 28.256

Xo 2 sqrt / 28.2843 V *

Full rectified sinusoid

t x Xo ω t * sin abs * :

X.rms t s * x N : X T x vectorize eval : X.Trms X norme X length sqrt / : X.F X fft : X.Frms X.F norme X.F length / : 51 line

T X augment X.rms 2 1 sys

X.rms 28.2843 V *

X.Trms 28.256 V *

X.Frms 28.256

Xo 2 sqrt / 28.2843 V *

Half rectified sin

t x Xo ω t * sin * ω t * sin 0 > (* :

X.rms t s * x N : X T x vectorize eval : X.Trms X norme X length sqrt / : X.F X fft : X.Frms X.F norme X.F length / : 51 line

T X augment X.rms 2 1 sys

X.rms 20 V *

X.Trms 19.98 V *

X.Frms 19.98

Xo 2 / 20 V *

Half rectified sin

t x Xo t To / frac * :

x frac x x trunc - :

X.rms t s * x N : X T x vectorize eval : X.Trms X norme X length sqrt / : X.F X fft : X.Frms X.F norme X.F length / : 51 line

T X augment X.rms 2 1 sys

X.rms 23.0362 V *

X.Trms 23.1402 V *

X.Frms 23.1402

Xo 3 sqrt / 23.094 V *

Fase to fase

t x Xo ω t * sin * Xo ω t * 23 / π * - sin * - :

X.rms t s * x N : X T x vectorize eval : X.Trms X norme X length sqrt / : X.F X fft : X.Frms X.F norme X.F length / : 51 line

T X augment X.rms 2 1 sys

X.rms 48.9898 V *

X.Trms 48.9653 V *

X.Frms 48.9653

32 / sqrt Xo * 48.9898 V *

Square

t x Xo t To / frac 0.5 > Xo - cases :

X.rms t s * x N : X T x vectorize eval : X.Trms X norme X length sqrt / : X.F X fft : X.Frms X.F norme X.F length / : 51 line

T X augment X.rms 2 1 sys

X.rms 40 V *

X.Trms 40 V *

X.Frms 40

Xo 1 / 40 V *

Alvaro