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LM4961LQ Datenblatt(PDF) 11 Page - National Semiconductor (TI) |
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LM4961LQ Datenblatt(HTML) 11 Page - National Semiconductor (TI) |
11 / 16 page Application Information (Continued) DUTY CYCLE The maximum duty cycle of the boost converter determines the maximum boost ratio of output-to-input voltage that the converter can attain in continuous mode of operation. The duty cycle for a given boost application is defined as: Duty Cycle = V OUT +VDIODE -VIN / VOUT +VDIODE -VSW This applies for continuous mode operation. INDUCTANCE VALUE The first question we are usually asked is: “How small can I make the inductor.” (because they are the largest sized component and usually the most costly). The answer is not simple and involves trade-offs in performance. Larger induc- tors mean less inductor ripple current, which typically means less output voltage ripple (for a given size of output capaci- tor). Larger inductors also mean more load power can be delivered because the energy stored during each switching cycle is: E = L/2 X (lp)2 Where “lp” is the peak inductor current. An important point to observe is that the LM4961 will limit its switch current based on peak current. This means that since lp(max) is fixed, increasing L will increase the maximum amount of power available to the load. Conversely, using too little inductance may limit the amount of load current which can be drawn from the output. Best performance is usually obtained when the converter is operated in “continuous” mode at the load current range of interest, typically giving better load regulation and less out- put ripple. Continuous operation is defined as not allowing the inductor current to drop to zero during the cycle. It should be noted that all boost converters shift over to discontinuous operation as the output load is reduced far enough, but a larger inductor stays “continuous” over a wider load current range. To better understand these trade-offs, a typical application circuit (5V to 12V boost with a 10µH inductor) will be ana- lyzed. We will assume: V IN =5V, VOUT = 12V, VDIODE = 0.5V, VSW = 0.5V Since the frequency is 1.6MHz (nominal), the period is ap- proximately 0.625µs. The duty cycle will be 62.5%, which means the ON-time of the switch is 0.390µs. It should be noted that when the switch is ON, the voltage across the inductor is approximately 4.5V. Using the equation: V = L (di/dt) We can then calculate the di/dt rate of the inductor which is found to be 0.45 A/µs during the ON-time. Using these facts, we can then show what the inductor current will look like during operation: During the 0.390µs ON-time, the inductor current ramps up 0.176A and ramps down an equal amount during the OFF- time. This is defined as the inductor “ripple current”. It can also be seen that if the load current drops to about 33mA, the inductor current will begin touching the zero axis which means it will be in discontinuous mode. A similar analysis can be performed on any boost converter, to make sure the ripple current is reasonable and continuous operation will be maintained at the typical load current values. Taiyo-Yudens NR4012 inductor series is recommended. MAXIMUM SWITCH CURRENT The maximum FET switch current available before the cur- rent limiter cuts in is dependent on duty cycle of the appli- cation. This is illustrated in a graph in the typical perfor- mance characterization section which shows typical values of switch current as a function of effective (actual) duty cycle. CALCULATING OUTPUT CURRENT OF BOOST CONVERTER (I AMP) As shown in Figure 2 which depicts inductor current, the load current is related to the average inductor current by the relation: I LOAD =IIND(AVG) x (1 - DC) (7) Where "DC" is the duty cycle of the application. The switch current can be found by: I SW =IIND(AVG) + 1/2 (I RIPPLE) (8) Inductor ripple current is dependent on inductance, duty cycle, input voltage and frequency: I RIPPLE =DCx(VIN-VSW)/(fxL) (9) combining all terms, we can develop an expression which allows the maximum available load current to be calculated: I LOAD(max) = (1–DC)x(ISW(max)–DC(VIN-VSW))/2FL(10) The equation shown to calculate maximum load current takes into account the losses in the inductor or turn-OFF switching losses of the FET and diode. 20094099 FIGURE 3. 10µH Inductor Current 5V - 12V Boost (LM4961X) www.national.com 11 |
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