Waveform Analysis
When a step function (Pulse) passes through the transformer/common mode
coil combination, it is modified by the parasitic parameters of the coils. To estimate the reshaping of the wave, the following formulas are used to calculate the Rise Time, the Overshoot, the Droop, the Fall Time, the Backswing, the Ringing and the Recovery Time.
Rise Time
Based upon circuit analysis of the transformer model, mathematically the following formula is derived to estimate the rise time based upon the calculated Leakage Inductance and Distributed Capacitance of the coils.
FORMULA:
EXAMPLE:
Where: RS = RL = 100 ohms n = 1:1 LL = 0.289 uh
CD = 1.152 pf
Overshoot
Overshoot on the leading edge of the waveform is controlled by the
distributed capacitance and leakage inductance of the coils. The leakage inductance has the greatest effect. If the leakage inductance is very low, then the rise time is fast and the leading edge shoots past the intersection of the rising portion and the pulse top lines. If the distributed capacitance is low, then there is the possibility of ringing at the end of the leading edge.
FORMULA:
Where: CD = pf and LL = uh
EXAMPLE:
K = 1.8414
Wave-top Droop:
The top of the square wave looses its flatness due to the introduction of the open circuit inductance of the transformer.
The new top level at the end of the pulse is calculated using the following formula.
FORMULA:
EXAMPLE:
Backswing Voltage:
The backswing voltage is dependent upon the magnetizing current produced by the open circuit inductance of the primary when the voltage pulse is applied.
Magnetizing current – Im
Where: EC = coil voltage tW = pulse width
LP = pulse inductance of the coil
Where: RC = parallel equivalent core loss resistance
EXAMPLE:
Recovery Time
The pulse recovery time is dependent upon the primary inductance of the coil and the parallel equivalent resistance of the core loss resistance and the load resistance of the circuit.
9.5.2FORMULA:
EXAMPLE:
Cutoff Frequency
Where the low frequency rolloff is determined by the open circuit inductance, the high frequency cutoff is determined by the leakage inductance and the distributed capacitance. These are typically 3 db rolloff points.
Low frequency rolloff
fo = RE / ( 2*π*LP )
where
High frequency rolloff
Hz