#Let's learn about power supply#Lesson 2: Derivation of the calculation formula for the duty cycle of the BUCK circuit
In the first lecture of #Let's learn about power supply#: Introduction to Buck circuit , we introduced that the BUCK circuit is a step-down circuit, and its most basic use is to achieve the conversion from relatively high voltage to low voltage. Then the relationship between input and output voltage (that is, the conversion calculation of input and output voltage) becomes the key to designing the BUCK circuit.
Buck circuit input and output voltage relationship
So, what is the input-output voltage relationship of the Buck circuit? Here we give a formula for the input-output voltage relationship:
Vo= Vin * D
Vo is the output voltage
Vin is the input voltage
D is the duty cycle
Duty cycle definition and formula derivation
The concept of duty cycle is introduced in the above input-output relationship formula. Most netizens should be familiar with the duty cycle, but in order to ensure the completeness of our content and the duty cycle is an important part in the Buck circuit, we will first give you a brief introduction to the duty cycle.
Duty cycle refers to the ratio of the duration of a high-level signal in a periodic signal to the period. It is the ratio of the occupation time of a high-level signal in a pulse signal to a complete cycle time. Duty cycle is usually expressed as a percentage and is widely used in control circuits and power circuits.
We will use the waveform diagram to derive the calculation formula for the duty cycle.
figure 1
From Figure 1 we can easily get:
The waveform period of the corresponding periodic signal is T = Ton + Toff;
Where Toff is the low level time of the waveform, and Ton is the high level time of the waveform.
Then the definition expression of duty cycle D is
;
That is, the ratio of the time of high level in one cycle.
The square wave we usually talk about (unless otherwise specified) has a duty cycle of 50%. For example, the active crystal oscillator and signal generator we use have a default duty cycle of 50%. (The duty cycle of the signal generator is adjustable).
Then the frequency of the waveform is the inverse of the period
.
Derivation of the input-output voltage relationship formula
After introducing the duty cycle, let's talk about the derivation process of the input-output voltage relationship formula Vout = Vin * D, so that everyone can better understand each parameter in the calculation through specific derivation.
The following calculations are based on the calculation of constant load parameters when the buck circuit enters steady state and the inductor is in continuous conduction mode.
Buck simulation circuit and corresponding simulation waveform built with SIMPLIS software ( the same as the simulation circuit and simulation waveform in the previous lecture )
image 3
First, let's look at the waveform of the inductor IL in the simulation example above.
Figure 4
The waveform of the inductor IL is shown in FIG4 , where Io is the average current value of the inductor, ILmax is the maximum current of the inductor, and ILmin is the minimum current of the inductor.
For ripple current engineering, take (0.3-0.5)Io
K is the current ripple factor
Figure 5
As shown in Figure 5, the inductor current reaches its maximum value at t = t0.
When Q is turned off, the inductor current gradually decreases
When t = t1, the inductor current reaches its minimum value.
The increase and decrease of the inductor current in one cycle are equal, that is,
Now we have completed the derivation of Vo = Vin*D. This formula reflects the relationship between input voltage, output voltage and duty cycle.
Input and output voltage calculation formula example application
After deriving the input and output voltage calculation formulas, let's do some example calculations to consolidate them.
Example 1: The input voltage range of a PWM modulation mode buck voltage conversion chip is 9-36V, and the output voltage is required to be 5V;
By knowing the conditions, we can reversely calculate the range of the IC's duty cycle under the conditions of Example 1:
Inductance calculation
Both of the above formulas can calculate the value of the inductor in continuous conduction mode;
Calculate the maximum diode current and diode reverse voltage
Calculate the maximum diode current by
▲I is the ripple current engineering (0.3-0.5)Io
ILmax = 1.5Io;
The reverse voltage of the diode is equal to Vin (when Q is turned on);
When selecting for actual projects, the withstand voltage and current of the diodes should be slightly larger than the actual calculated parameters, taking into account surge and engineering margin. Generally, about 2 times the calculated parameters are selected. (When the circuit environment is harsh, it is considered to add varistors, TVS and other protective devices at the power supply end).
Now let's verify the inductance calculated by our formula. Let's try it together.
Click "Inductor Selection Tool" under the "Design" menu on the web page and enter the following parameters. The inductance is 9.72uH
Let's calculate it using our formula
= ((12-5)*(5÷12)*0.2*0.00001)/(2*0.3)H
= 7*5*2*0.000001/(2*12*0.3)H
=70/7.2 H
=9.72 uH (rounded to 9.72, actual value 9.7222222…)
= 2+2**0.3 = 2.3A, which is exactly the same as the calculation by the official software.
In this issue, we talked about the calculation formula of the input and output voltage of the Buck circuit and the concept of duty cycle. We introduced in detail the derivation process of multiple formulas involved in the article. If there are any omissions or questions during the explanation, please post them and discuss. What knowledge points of the Buck circuit do netizens want to know most? Come and post to talk about it!
This concludes this issue. In the next issue, we will discuss the calculation of the output capacitance of the Buck circuit!
Final Thoughts
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Scan the QR code to add Guanguan’s WeChat account as a friend, and note “Switching Power Supply Interest Group” to invite him to join the group.
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