Appendix D: Sample Waveform Library

Constants

k0 indicates the half width ￿W50￿ for the pulse; k1 indicates the peak location

 

of the pulse.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Description

The waveform generated when the pulse width is taken to be tW50 and the

 

peak location is taken to be 0 can be expressed as

 

 

 

 

 

V￿t￿3 +3 exp3 ￿￿In￿2￿3 @3 ￿

2t

￿2￿3 Substituting3 s3 +3

 

tw50

3 gives

 

 

 

 

 

 

 

 

 

 

 

 

tw50

2 ￿23 In￿2￿

 

 

f￿t￿3 +3 exp3 ￿￿3

t2

￿, 3 and3 taking3 the3 Fourier3 transform3 gives

 

 

 

 

 

 

 

2s2

 

 

 

 

 

F￿jw￿3 +3 ￿

 

s3 @3 exp3 ￿￿3

w2s2

￿.3 This3 shows3 that3 this3 signal3 has3 a

 

2p

 

 

 

2

 

 

 

 

 

 

Gaussian form in the frequency domain as well.

 

 

 

 

 

<Example> When tw50 is 1 ms, the bandwidth will be 31.2 kHz.

 

 

 

 

 

 

 

Settings

Waveform points: 256

 

 

 

 

 

Clock frequency: 100 MHz

 

 

 

 

 

Output time: 2.56 ms

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

D￿4

AWG2021 User Manual