SMPS Transformer Primary Inductance

Question

When Designing SMPS we calculate all the parameter on minimum DC bus voltage (eg 85Vac*1.414=100VDC), and we get require inductance for primary winding is Lp (eg 0.97mH). But in real we run on Normal nominal line ( eg 240*1.414=340), so as per calculation I observe we require inductance change to 3.2mH. How this extra inductance will be compensate.

As i understand at minimum DC volt what we get is Max primary inductance.

Formula used Vrefleccted=110V Fsw=100Khz Pi=14W Dmax=Vref/(Vref+VDCmin) Ip=2*Pin/(VDCminDmax) Lpri=VDCminDmax/(IpriXFsw)

Case 1:- When VDC=100V (Minimum DC) Dmax=0.5, Ip=0.53A, Lpri=0.9mH

Case 2:- When VDC=340V ( Normal Line) Dmax=0.24, Ip=0.33A, Lpri=2.4mH

So as DC bus volt goes up, require ind increase then why we calculate Inductance using minimum DC bus voltage.since all winding is fixed at low Vdc calculation.

Answer 1

At the lowest bus voltage, the duty cycle of the switching needs to be close to maximum on full output load. As bus voltage rises, duty cycle lowers to keep the output voltage (across the load) regulated. You don't appear to have factored this into your analysis correctly. If bus voltage doubles, roughly speaking, the duty cycle will halve so that it maintains the same energy transfer per switching cycle through the transformer and on to the load.

As an example, if your primary inductance is 1 mH and the switching frequency is 100 kHz, the current in the primary will reach a peak of 0.5 amps after 5 us. This assumes a bus voltage of 100 V and a duty of 50%. It's just a rearrangement of V = L di/dt. Solve for di etc..

This also tells me that the energy transferred per cycle (assuming a discontinuous situation) is 0.125 mJ and, at a switching frequency of 100 kHz, this is equivalent to a power transfer of 12.5 watts. This will be the power you have estimated going into your load with an extra bit for the inefficiences of the power supply. I guess you are running about 10 watts to your load.

As the bus rises you won't want that power to change. So, if the supply voltage doubles you will still want 12.5 watts (approximately) passing through the transformer. At twice the voltage, the current will double of duty cycle remains the same and this means 4x the energy transferred per cycle hence, duty must halve so that the peak current remains the same. So, for a 200 V bus, duty will be 25% and, for a 340V bus duty must fall to about 15% and not 24% as implied in your question.