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AN3400 Datasheet(PDF) 46 Page - STMicroelectronics |
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AN3400 Datasheet(HTML) 46 Page - STMicroelectronics |
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46 / 78 page  Modeling of the dead time after the NPN storage time phase AN3400 46/78 Doc ID 018840 Rev 1 phase, the following system of two first order linear differential equations is valid on all the [t5,t6] time interval with C=Cn=Cp: System of equations 19 in which VBEn= −VCEBn<0 and VEBp= −VCBEp<0 is an opportunely modeled signal complying with the following function: Equation 24 in which ψ 1 is a constant depending on the initial value of the VCEBn voltage at t=t5-. The length of this dead time interval fixed for the simulation, in which the VCn and VCp voltage functions are determined through the ODE45 simulator, is imposed to be given by the following formula in which Tnpnsto=t5−t4, Tnpncon=t4−t2 and Tnpnric=t2−t0: Equation 25 This last working operation phase described completes the resonant driving network modeling with reference to the variation over a one-half period of the voltage signal V(s) across the filter capacitor and in particular concerning the time intervals, in sequence, shortly before (re-circulating phase), during (conduction phase) and afterwards (dead time) the NPN bipolar device functional stage. In the second one-half period the voltage signal V(s) has an opposite polarity compared to the first one and an analytical procedure similar to the NPN device modeling technique is applied for the PNP bipolar device interested in being simulated during its sequential working condition phases, as subsequently shown. () () S CEBn S S CBCp npndead Cp b npndead Cn b S npndead Cn R C V R C V I C V R C V R R C t V dt d ⋅ + ⋅ + ⋅ + ⋅ ⋅ − ⋅ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + ⋅ − = − − − 1 1 1 1 1 () () S CEBn S S CCBn npndead Cp b npndead Cn b S npndead Cp R C V R C V I C V R C V R R C t V dt d ⋅ − ⋅ − ⋅ − ⋅ ⋅ − ⋅ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − ⋅ = − − − 1 1 1 1 1 () () = 5 5 − − + − t V t V npnsto Cn npndead Cn () () = 5 5 − − + − t V t V npnsto Cp npndead Cp 1 S CS CBnpn CCBn CEBn t C I C I = V ψ + ⋅ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − npnric npncon npnsto 5 6 npndead T T T f 2 1 t t = T − − − = − |
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