I'm struggling to find a textbook formula where the 100Hz ripple across the choke in a LC filter duty can be calculated, in the condition the minimum critical current value across the circuit is satisfied.
By doing some simulations with PSUD2, I've come to the following conclusions:
-The transformer secondary Vrms value is proportional to the choke Vrms ripple value, by an approximate factor of 2.2. Is there any formula that justifies this?
-The simulations also show this ripple is almost entirely dependent of the transformer secondary voltage and the other components values can be considered negligible. A significant alteration of the ripple value though is the running from minimal critical current conditions.
By doing some simulations with PSUD2, I've come to the following conclusions:
-The transformer secondary Vrms value is proportional to the choke Vrms ripple value, by an approximate factor of 2.2. Is there any formula that justifies this?
-The simulations also show this ripple is almost entirely dependent of the transformer secondary voltage and the other components values can be considered negligible. A significant alteration of the ripple value though is the running from minimal critical current conditions.
Or another way I saw it through simulations:
the transformer secondary Vrms is almost equal to the Vp-p ripple across the choke. But this gives a factor of 2.82. Perhaps the RMS value of this ripple has another waveform coefficient? Harmonic distortion?
audiofilterchokes-page2
On this Turneraudio choke input article, Fig 1., it is claimed the ripple contains some THD. My personal measurements of the harmonic content of choke input ripples also contributes to similar results, in the 10 to 15% range of even harmonics. Rough results that depend of the magnetization conditions of the core. Due to the DC current through the choke, it is logical the dominant harmonics should be even.
the transformer secondary Vrms is almost equal to the Vp-p ripple across the choke. But this gives a factor of 2.82. Perhaps the RMS value of this ripple has another waveform coefficient? Harmonic distortion?
audiofilterchokes-page2
On this Turneraudio choke input article, Fig 1., it is claimed the ripple contains some THD. My personal measurements of the harmonic content of choke input ripples also contributes to similar results, in the 10 to 15% range of even harmonics. Rough results that depend of the magnetization conditions of the core. Due to the DC current through the choke, it is logical the dominant harmonics should be even.
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Just wild guessing and thinking.
The Vrms to Vdc voltage ratio of a critically loaded LC filter is 0.9
1 / (0.9/2) - 2.22
The Vrms to Vdc voltage ratio of a critically loaded LC filter is 0.9
1 / (0.9/2) - 2.22
You are basically asking 'what is the magnitude of the fundamental component in a full-wave rectified sine wave?'. Calculus provides the answer. You may find an online calculator, or someone somewhere must have done the calculation.
I would do a rough estimate as follows:
We know that the input has a peak value of 1.414 x Vrms.
We know that the mean (i.e. DC) value is 0.9 x Vrms.
Therefore the positive peak ripple is 0.515 x Vrms. Most of this will be the fundamental at twice the mains frequency, so estimate something in the region of 0.4-0.5 x Vrms i.e. a ratio of 2-2.5 smaller than the input.
I would do a rough estimate as follows:
We know that the input has a peak value of 1.414 x Vrms.
We know that the mean (i.e. DC) value is 0.9 x Vrms.
Therefore the positive peak ripple is 0.515 x Vrms. Most of this will be the fundamental at twice the mains frequency, so estimate something in the region of 0.4-0.5 x Vrms i.e. a ratio of 2-2.5 smaller than the input.
Assuming a single secondary winding with voltage Vrms, and ideal bridge rectifier and choke and large output filter capacitance, then input voltage to choke has:
- a DC level of 0.9 x Vrms
- an AC level of 1.27*Vrms/(n^2-1), where n=2,4,6.. (ie. the even harmonics of the mains frequency) and determined by fourier analysis. This is approx 0.42 x Vrms, based on just 2nd harmonic and assuming harmonics rapidly reduce.
Note that the critical inductance in H is approx R/(6.pi.f), where R is load in ohm. This is based on the peak ripple current from 2nd harmonic not exceeding the load DC current, and assumes higher frequency ripple is suppressed.
Example would be 500Vrms secondary, with 450Vdc. A 100mA load would give R = 4500 ohm, and so critical inductance of approx 4.8H for 50Hz mains. PSUD2 shows agreement.
Note that as a supply voltage, your mains waveform likely has a fair bit of harmonic distortion. So given choke inductance variation with current, and the harmonics floating around, these rules of thumb are approximations.
- a DC level of 0.9 x Vrms
- an AC level of 1.27*Vrms/(n^2-1), where n=2,4,6.. (ie. the even harmonics of the mains frequency) and determined by fourier analysis. This is approx 0.42 x Vrms, based on just 2nd harmonic and assuming harmonics rapidly reduce.
Note that the critical inductance in H is approx R/(6.pi.f), where R is load in ohm. This is based on the peak ripple current from 2nd harmonic not exceeding the load DC current, and assumes higher frequency ripple is suppressed.
Example would be 500Vrms secondary, with 450Vdc. A 100mA load would give R = 4500 ohm, and so critical inductance of approx 4.8H for 50Hz mains. PSUD2 shows agreement.
Note that as a supply voltage, your mains waveform likely has a fair bit of harmonic distortion. So given choke inductance variation with current, and the harmonics floating around, these rules of thumb are approximations.
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Hello,
Lundahl writes in their PDF power supply choke data sheets that ripple voltage is about 42% of the input voltage.
Greetings, Eduard
Lundahl writes in their PDF power supply choke data sheets that ripple voltage is about 42% of the input voltage.
Greetings, Eduard
Excellent explanations! Thanks a lot, guys!
If you don't mind answering, in which book these answers can be found?
If you don't mind answering, in which book these answers can be found?
A relatively recent reference that extends across most areas is from Motorola, now Onsemi:
http://www.introni.it/pdf/Motorola%20-%20Rectifier%20Applications%20Handbook.pdf
Waveform analysis is all based on standard maths and fourier analysis.
http://www.introni.it/pdf/Motorola%20-%20Rectifier%20Applications%20Handbook.pdf
Waveform analysis is all based on standard maths and fourier analysis.
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