Electromagnetic pulses generated via the use of photodiodes are inevit
ably a composite of exponential decay transients due to the finite lif
etime of the charge carriers and RC relaxation times of the triggering
circuit. We have developed a microwave technique in which the limitin
g factor of the pulse lineshape is governed by the coupling between a
slot and microstrip transmission line instead of exponential transient
s. The coupling involves the overlap of these two lines in which one l
ine launches the pulse and the other receives it. We have measured mos
tly electromagnetic pulses with Gaussian lineshape in agreement with o
ur calculations. The formulation of the calculation involves a Lagrang
ian description of the coupling between these two lines.