The waveform shown in a sweep voltage used to defect the

The waveform shown in a sweep voltage used to defect the beam in a cathode ray oscilloscope. The transform of this function can be written as—

In order to calculate the L.T. of periodic saw took waveform use the relation given below.

F(s) =	F₁(s)
	1 −e^−Ts

where F₁(s) = Laplace transform of the single waveform
T = Time period of the given wave
Calculation for F₁(s)

F₁(t) =	1	t r (t) −	1	(t − a) r (t − a) − 1 u (t − a).....(i)
	a		a

taking Laplace transform both side, we get

F₁(s) =	1	−	1	e^−as	−	1	e^−as
	as²		a	s²		s

Time period (T) = a

Now F(s) =	F₁(s)
	1 − e^−Ts

or F(s) =	1	−	e^−as
	as ²		s (1 − e^−as)

F (s) =		1	-	e^–as
		as²		s(1 – e^–as)

F (s) =		1	-	e^–as
		as		s(1 – e^–as)

F (s) =		1	-	e^as
		as²		s(1 – e^–as)

F (s) =		1	-	e^–as
		as²		s(1 + e^–as)