Thursday, 15 March 2012

 Average current-mode control (CMC) requires that the total waveform of the current be reconstructed for the control loop. This article presents the steps required to select the transformer and how to design the circuit needed to meet the end use in a manner that prevents transformer saturation. The model we used is a power factor correction (PFC) topology. A commercially available current-sense transformer is used in this analysis to identify the parameters needed and how to use this information to design the circuit in order to prevent saturation.
To meet the objective of reconstructing the current signal needed for PFC average CMC means that both the current during the power pulse (“on” time) and the current during the freewheeling energy recovery time (“off” time) must be included in the generated current signal. In higher-power PFCs the losses through a resistive sensor system become significantly high, so current transformers are used. In this analysis we demonstrate the design of the current transformers needed in a PFC circuit because it will be more demanding as compared to a standard forward converter.
Analysis
Table 1 lists specific details needed to identify the two current transformers to be used in this converter. The IinLpk current indicates that the current transformer needed has a primary current handling capability of approximately 20 A and a switching frequency of 100 kHz. A pulse PA 1005.100 transformer with a primary current handling capable of 20 A and a frequency range of 50 kHz to 1 MHz meets the requirements for this design.
Table 1: Parameters needed to generate a PFC design.
Table 2: Current transformer datasheet specifications
These two tables give us the information needed to identify several parameters, including the peak current and the resistance on the sense resistor, voltage across the secondary, total voltage across the inductor, duration this voltage is present, change in the magnetizing current, and the transformer value.
The peak current on the secondary is easily determined as (Eq 1):
IRsenseL = IinLpk / N = 0.183 A
The resistance of the sense resistor can be determined from (Eq 2):
R1 = VRsense /IRsenseL = 5.464 Ω.
The voltage across the secondary, assuming that the converter is operating at maximum load and minimum input voltage, can now be determined. This total voltage consists of the voltage across the current-sense resistor, Rsense, which by definition is 1 volt, the voltage across the diode which again is defined at 0.7 volts and the voltage across the winding resistance VRwinding can be calculated as (Eq 3):
VRwinding = Rwinding * IRsenseL = 1.007 V
The total voltage across the inductor can now be calculated as (Eq 4):
Vind = VRsense +Vfd + VRwinding = 2.707 V
The duration this voltage is present across the magnetizing inductance is (Eq 5):
TonL = DL / Fosc = 6.995 µs
The change in the magnetizing current in the magnetizing inductance is (Eq 6):
∆Imagpk = (TonL * Vind) / Lmag = 9.466 mA
At this point you need to verify that the transformer is below the saturation level. The formula given for that can now be populated with the derived values (Eq 7):
Bpk = (37.59 * Vind* DL*105)/(N*Fosc*10-3) = (37.59 * 2.707 * 0.699 * 105)/(100 * 105 * 10-3) = 711.6
This is about 30% of the maximum allowed flux level, which, according to the datasheet, is 2,000.
Since the flux density developed in the worst case conditions for this configuration is less than half the flux level that would result in saturation, the magnetizing current can be allowed to increase (in this case almost by a factor of three), as long as it can be reduced sufficiently in the “off” time.
To keep the transformer from “walking” into saturation, you need to develop a volt second integral during the time that Q1 is off. This will balance the volt-second integral during the “on” time. This is done by having a resistor R1 (which can be referred to as the reset resistor) in place so that the magnetizing current developed during the “on” time will force a voltage to develop across this reset resistor (R1) during the “off” time. It is important to remember that the voltage across this resistor will decrease as the magnetizing current decreases.
To determine the value of R1, set the peak magnetizing current to 2 * ∆Imagpk and design the circuit so that during the “off” time the resistor chosen will reduce the magnetizing current to 0.5 * ∆Imagpk. This will ensure operation where the peak current is less than 2 * ∆Imagpk.
Set the initial current through the magnetizing inductor to Iinit = 20 mA set the final magnetizing current to Ifinal = 5 mA. The off time is determined as Toff = 3.005 µs and the magnetization inductance, Lmag, of the chosen transformer is 2 mH (from the datasheet). This is sufficient information to get the value of the R1 resistor (Eq 8).
R1= ((ln(Iinit/Ifinal)) * Lmag) / Toff) = ((ln(4)) * 2 mH) / (3.005 µs) = 922.6 Ω
At this point the solution is half done. You still need to address the design of the current transformer circuit for the boost diode current sensor. The worst case conditions for the T2 current transformer is the peak of the maximum line voltage with the maximum load.
The “off” time for the main switch at the peak of high line is the maximum conduction time of the rectifying diode, D3, and the primary of the T2 current transformer. This is the condition that will be used in the design.
Since the same developed voltage across the current-sense resistor for the same primary current in needed, the same Rsense is used for both transformers. The conduction time for the current through the primary of T2 is (1-D). The maximum conduction for the transformer primary can be determined by (Eq 9):
Tondiode = (1-DH) / Fosc = 9.369 µs
The corresponding reset time for the transformer is (Eq 10):
Toffdiode = DH / Fosc = 0.631 µs
The current through the T2 transformer primary under these conditions (maximum input voltage) is considerably less than at the low input voltage. The maximum current, IinHpk, is only 5.87 A at the high line.
This yields a voltage across the sense resistor under these conditions (Eq 11):
VRsencehigh = (IinHpk / N) * R2 = ((5.87 A) / 100) * 5.464 Ω = 0.292 V
The voltage across the internal winding resistance is (Eq 12):
VRwindingH = (IinHpk / N) * Rwinding = 0.294 V
The voltage across the transformer magnetizing inductance is equal to (Eq 13):
VmagHigh = VRsencehigh + Vfd + VRwindingH = 0.292 V + 0.7 V + 0.294 V = 1.285 V
Calculating the flux in the core for a single pulse is (Eq 14):
BpkH = (37.59 * VmagHigh * (1-DH) * 105) / (100 * Fosc *10-3)
= (37.59 * 1.285 * .937 *105) / (100 * 105 *10-3) = 452.6
The flux is about 25% of the allowable flux.
The magnetizing current is determined as (Eq 15):
ImagH = (VmagHigh * Tondiode )/ Lmag = (1.285 V * 9.369 µs) / 2 mH = 6.02 mA
If we now set the limits for the magnetizing current as the peak being twice ImagH and the final as being half of ImagH and the time as being TresetH where TresetH = DH/Fosc, we can determine the value of R2 by (Eq 16).
R2 = ((ln(2/.5)) *Lmag) / TresetH = (1.386 * 2 *10-3 ) / (.631 * 10-6) = 4.395 kΩ
This completes the design of the current-sense circuit for the PFC circuit. Similar calculations would be required for average current-mode control of a buck converter. For peak current-mode control of a buck converter, only the above calculations are needed, with the main switch duty cycle limits being used at maximum load and minimum input voltage.

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