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what will happen to the indictor value when we increase the switching frequency of the smps?

At higher switching frequencies, the inductor and capacitor size gets reduced. Other things will remain the same. The power converter behaviour will remain the same. i.e. It will give the same output at every frequency.

In SMPS (Switched-Mode Power Supplies), the frequency of operation is closely related to the inductance of the inductor used in the circuit. This relationship arises due to the way SMPS operates, typically using a switching regulator topology such as buck, boost, or buck-boost.

1. **Buck Converter**: In a buck converter, the output voltage is lower than the input voltage. During operation, the inductor stores energy when the switch (typically a MOSFET) is on, and releases this energy to the output when the switch is off. The switching frequency determines how fast this process occurs. Higher frequencies allow for smaller inductors to be used because they can transfer energy more quickly.

2. **Boost Converter**: In a boost converter, the output voltage is higher than the input voltage. Similar to the buck converter, the inductor stores energy during the switch-on time and releases it to the output when the switch is off. Again, the switching frequency affects the rate at which energy is transferred, thus influencing the required inductance.

3. **Buck-Boost Converter**: In a buck-boost converter, the output voltage can be higher or lower than the input voltage, depending on the duty cycle of the switch. The operation principles regarding the inductor and frequency are similar to those of the buck and boost converters.

In general, the relationship between frequency and inductance in an SMPS can be summarized as follows:

- Higher frequencies allow for the use of smaller inductors.
- Lower frequencies necessitate larger inductors.
- The choice of frequency depends on various factors including desired efficiency, size constraints, cost, and electromagnetic interference (EMI) considerations.

It's important to note that the choice of frequency in SMPS design involves trade-offs. Higher frequencies can lead to higher switching losses and EMI, while lower frequencies may result in larger and more expensive components. Therefore, designers need to carefully select the operating frequency based on the specific requirements of the application.


for example

In order to quantify the problem, let us assume that the passive elements are those reactive elements such as Inductors and capacitors used to perform voltage conversion and filtering operation. As the frequency is up scaled by factor m then the inductor will be scaled by 1/m , and also the capacitor will be scaled by 1/m to scale the cut frequency of the filter by m. This can be get out from the fact that the resonance frequency w0^2= 1/LC. So, it is clear from this relation that if wo is scaled by m , both L and C are scaled by 1/m as i assumed in the beginning of the post.
Now let us assume that the supply Vs operates at the same Voltage, to supply the same power to a resistive  load RL. So the problem is now defined. One can calculates the current in the inductance assuming that the whole voltage will be dropped on it , then 
The current in the inductor IL= Vs/ jwLi where Li initial inductance. Scaling the frequency by m then IL scaled= Vs/ jwm Li /m= IL, so the current will not change by the scaling. 
The power dissipation will become= IL^2 scaled Rl with Rl is self-resistance of the coil.
The self resistance of the coil is proportional to its number of turns N. It is known that the inductance L is proportional to N^2, so  Rl will be scaled by 1/ sq. root of m.,
So the power dissipation in the inductor will be scaled by 1/ sq. root of m under the given assumptions. If the resistance is made initially small there will be no appreciable temperature rise by scaling the inductor. The power density per volume and the surface area of the component can be designed to keep the temperature the same.
As for the capacitor, as it is nearly ideal its losses will be small and the temperature rise by frequency scaling may be negligible.
More rigorous analysis is required to quantify the problems but according to these estimations it is not very serious.

The increase in switching frequency leads to have the following loses .

1.power losses 

Switching frequency can be an important factor on power loss for a buck converter. Three dominant power losses are identified as: switching loss, conduction loss, and driver loss. This section provides the brief formula based on buck converter.

2. switching losses 
            Switching losses are associated with the transition of the switch from its on-state to off-state, and back.
3.conduction losses 

4.Drive losses    
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