# Fundamental of power electronics

#### skhattak

Joined Nov 15, 2011
3
Hi All,

Can anyone help me in solving the following question.
To reduce the switching harmonics present in the input current of a certain buck converter, an input filter
consisting of inductor and capacitor is added as shown in Fig. 2.32. Such filters are commonly
used to meet regulations limiting conducted electromagnetic interference (EMI). For this problem, you
may assume that all inductance and capacitance values are sufficiently large, such that all ripple magnitudes
are small.
(a) Sketch the transistor current waveform

(b) Derive analytical expressions for the dc components of the capacitor voltages and inductor currents.

(c) Derive analytical expressions for the peak ripple magnitudes of the input filter inductor current
and capacitor voltage.

(d)
Given the following values:
Vg= 48 V
V=36 v
f= 100 kHz
R=6 ohms

Select values for and such that (i) the peak voltage ripple on is two percent of the dc
component and (ii) the input peak current ripple is 20mA.
Extra credit problem: Derive exact analytical expressions for (i) the dc component of the output voltage,
and (ii) the peak-to-peak inductor current ripple, of the ideal buck-boost converter operating in
steady state. Do not make the small-ripple approximation.
Circuit is attached.

#### crutschow

Joined Mar 14, 2008
27,755
We're not going to solve this for you. You need to tell us what you have done so far.

Do you understand the fundamental operation of a buck converter?

#### bountyhunter

Joined Sep 7, 2009
2,512
Buck regulator operation explained on page 34:

#### Attachments

• 265.8 KB Views: 110

#### skhattak

Joined Nov 15, 2011
3
We're not going to solve this for you. You need to tell us what you have done so far.

Do you understand the fundamental operation of a buck converter?
Thanks for your prompt reply. I undersatnd the operation of buck converter but in the mentioned problem an input filter is added which make the solution a bit complex. if you can please draw the circuit fr sub interval 1 (0<t<DTs) and sub interval 2 (DTs<t<Ts).Then the solution will not be a problem.

Regards,
S Khattak

#### t_n_k

Joined Mar 6, 2009
5,455
This is quite a challenging problem that requires the designer to make some assumptions and presumably tweak the design if necessary to meet the specification.

What's the duty cycle D?
What's the mosfet switch on-time, Ton and the switch off-time , Toff at 100kHz.

The input filter must stabilize the source current to the extent that only 20mA ripple is allowed.

With a DC output of 36V into a 6Ω [=6A] load you need an average input current [at Vg=48V] of 4.5A. That's based on a simple power balance.

I would base my initial assumption around the concept that the combined effect of the input inductance with the 48V source is an equivalent constant current source of 4.5A.

One then must make some additional design assumptions. There are no constraints on the input filter capacitor ripple voltage. So you can decide on this to be whatever you wish - within reason. Alternatively you can decide on a capacitor value.

Suppose you assume the input filter capacitor ripple voltage is a modest 5V (pk-pk). That's a little more than 10% of the supply voltage.

With the mosfet switch off, the capacitor is charging with 4.5A. With the switch on, the capacitor must supply the deficit in load current - i.e. discharge at (6A-4.5A)=1.5A. The charging time is Toff. The discharge time is Ton.

So

I_charge=4.5A=C*ΔV/Toff

or

I_discharge=1.5A=C*ΔV/Ton

I've arbitrarily assumed a value of ΔV=5V [the aforementioned capacitor ripple voltage]. You might find 5V is too small or impractical - you might have to go to 10V say or an even smaller value (say 2.5V) - its' probably a matter of some trial and error to come up with a practical design. Practicalities would include a consideration of capacitor ESR & parasitic inductance values - matters beyond the present discussion but worth keeping in mind.

At this stage you could therefore find a suitable capacitor value.

Next comes working out a suitable input filter inductance - the tricky bit.

Having assumed the capacitor ripple voltage is 5V and having selected a value for the capacitor, I can now make an estimate of the required filter inductor value. There is an important condition that must be met in selecting the inductance. The specification calls for a maximum source ripple current of 20mA. I have decided the capacitor ripple voltage is 5V. The inductor must therefore support this capacitor ripple voltage [ΔV=5V] with a maximum ripple current of 20mA. That piece of information plus the known values of Ton and Toff, is the key to making an initial estimate for the inductance. Rather than give you the entire solution strategy I'll leave that important step for you to consider at your leisure.

Postscript:

I'd strongly advise using a circuit simulation package to do your trial and error work to confirm the aforementioned estimates are practical - otherwise you'll spend a lot of time proving on paper which options are workable. In particular it will help verify you are meeting the design specifications.

Last edited:
• amilton542

#### t_n_k

Joined Mar 6, 2009
5,455
Since the OP seems to have lost interest, I thought that others might find it useful to bring the input filter design to a conclusion.

Attachments show the partial schematic for the pre-filter LC section and the simulated waveforms for the source current and the inductor voltage. These are based on the arbitrary assumption of assigning a capacitor ripple voltage of 5V p-p. See my earlier post.

The source current Ig has an average value of 4.5A with a ripple of the order of 20mA p-p. The buck converter switching frequency is 100kHz at a duty cycle of 0.75. Hence Ton=7.5us and Toff=2.5us. Duty cycle is set at 0.75 to give a 'bucked' output of 36V.

How does one select the inductor L_filt value? C_filt would have been calculated from the assumed capacitor ripple voltage of Vr=5V as

C_filt=Ig[avge]*Ton/Vr =(4.5*2.5*10^-6)/5=2.25uF.

It's a relatively simple task to show that the inductor ripple current would be given by the relationship

Ig[ripple]=(1/L_filt)*(Vr/8)*(Ton+Toff)
Ig[ripple]=(1/L_filt)*(Vr/8)*Tsw=Vr/(8*fsw*L_filt)

where fsw and Tsw are the buck converter switching frequency and period respectively.

To obtain a ripple current of Ig[ripple]=20mA p-p one needs to satisfy the relationship

L_filt=Vr/(8*fsw*Ig[ripple])

giving

L_filt=5/(8*1E^5*20E-3)=312.5E-6 or 312.5uH.

So we then have for the pre-filter design C_filt=2.25 uF and L_filt=312.5uH

Other values would suit equally well depending on the value one allows for the ripple voltage Vr.

#### Attachments

• amilton542

#### amilton542

Joined Nov 13, 2010
497

#### t_n_k

Joined Mar 6, 2009
5,455