Pulse Width & Power Calculations

In order to prevent expensive damage to the probes or associated electronics, care must be excercised in setting power levels and pulse widths. For our Inova 500 spectrometer, maximum power corresponds to a setting of 63 dB. (Note that Varian follows the convention that increasing dB represents increasing power.) For 1H this represents 50 W; for 13C or 15N, however, 63 dB corresponds to an output of 300 W. Knowing this, the power can be calculated at any setting using the following equations:

dB(final) - dB(initial) = 10 log { power(final) / power(initial) }.

For example, we can calculate the power used if the 1H channel is set to 60 dB:

60 - 63 = -3 = 10 log { x/50 }

-0.3 = log { x/50 }

10 e -0.3 = antilog ( log {x/50})

50 ( 0.50 ) ~ 25 W

Since pulse widths are proportional to the voltage in the probe coil, and power is proportional to the square of the voltage (or current), we should be able to calculate the pulse width at a different power level. Since Varian uses the convention that increasing the dB increases the power, rather than attenuating the power, we have:

dB(final) - dB(initial) = 20 log { pw(initial) / pw(final) }.

For example, if the 1H pw at 51 dB is 9.4 usec, we can calculate the pw at 45 dB:

45 - 51 = -6 = 20 log { 9.4/x }

-0.3 = log { 9.4/x }

10 e -0.3 = antilog ( log { 9.4/x })

x = 18.775 ~ 18.8 usec

Thus, a change of 6 dB corresponds to a 2-fold change in pulse width, but a 4-fold change in power.

Note that for our 1H amplifier 1 W corresponds to a dB setting of ~ 46 dB, whereas 1 W would correspond to ~38 dB for our 13C / 15N amplifiers.