Understanding Inductance (L) and Current (I) in SMPS Design

The heavy and inefficient transformers of traditional linear power supplies have nowadays been replaced by highly compact and efficient Switch Mode Power Supplies (SMPS). The driving force behind SMPS technology, which we encounter everywhere power is controlled—from our computer chargers to industrial machines—is high-frequency energy transfer.

The main actor in this transfer process is the inductor (coil). In an SMPS design, the relationship between the coil's inductance (L) value and the peak current (I) flowing through it determines the system's power, stability, and size. In this article, we will examine the delicate balance between these two variables in the SMPS architecture.

The Foundation of Energy Transfer in SMPS Systems

In SMPS circuits, the process of stepping down or stepping up voltage is accomplished not by a continuous flow of energy, but by a switch (usually a MOSFET) turning on and off at very high speeds (at frequencies ranging from kHz to MHz).

The system operates in two main phases:

1. Charge (Ton) Phase: The switch closes, and the current drawn from the input passes through the coil. The coil ramps up the current (linearly) with the voltage applied across it and stores energy in its magnetic field according to the rule U = 1/2 × L × I².
2. Discharge (Toff) Phase: The switch opens, and the connection to the input is severed. The coil opposes the cessation of the current flowing through it and discharges its stored magnetic energy to the output (to the load and the output capacitor).

By repeating these two cycles thousands of times a second, the desired uninterrupted power is achieved at the output. Therefore, the maximum power the system can deliver to the output is directly proportional to how much energy the coil can store in each cycle and how fast this cycle is repeated.

Determining the Minimum Inductance (L)

For an SMPS designer, one of the first and most critical calculations is finding the "Minimum Inductance" value. If the selected L value is too low, the current across the coil will rise very rapidly (high di/dt). This condition causes the circuit to reach Core Saturation, potentially burning out the transistors due to overcurrent. At the same time, a very low inductance drastically increases the current ripple, shortening the life of the output capacitors and causing noise in the output voltage.

If the L value is chosen to be unnecessarily large, this time the coil reaches massive dimensions, costs increase, efficiency drops due to higher internal resistance (DCR), and the system begins to respond very slowly to load changes (transient response).

When calculating inductance, the targeted ripple current (usually between 20% - 40% of the maximum load current) is taken as a reference. However, after this selection is made, the energy storage capacity of the system must definitely be verified.

Using the Calculation Tool in Design Analysis

When verifying your design, you can also use our Inductor Energy Calculator tool for reverse engineering.

A Practical Analysis:
Let's say that due to your system's frequency and power requirements, at least 250 µJ (microjoules) of magnetic energy must be stored in the coil during each charge phase. The peak current (Ipeak) that the MOSFETs and the general structure in your system can withstand is limited to 7 Amperes by design constraints.

Under these conditions, to find the minimum inductance (L) suitable for the design, you can use the "Calculate Inductance (L)" mode of the tool:

• Energy (U) = 250 µJ
• Current (I) = 7 A

The tool solves the formula as L = 2U / I² and will give a result of approximately 10.2 µH.
This result tells the designer the following: To safely store the targeted energy within the specified current limit, you must use a coil of at least 10.2 µH in your circuit. Selecting a coil with an industrial standard value of 15 µH or 22 µH (provided that the saturation current is greater than 7A) will ensure your design stays in the safe zone.

Continuous and Discontinuous Conduction Modes (CCM vs DCM)

In SMPS coil design, the relationship between inductance (L) and current (I) directly dictates the converter's operating mode (CCM or DCM).

CCM (Continuous Conduction Mode): If the coil is chosen to be large (high L value), a new charging cycle begins before the current ever drops to zero while the coil discharges its energy to the output. In this mode, the output ripple is low, but the coil being continuously under energy (core loss) must be accounted for.
DCM (Discontinuous Conduction Mode): If the coil is chosen to be smaller, it completely empties its energy and the current flowing through it drops to zero before the charge phase arrives. In this case, every cycle starts from zero current (Zero Current Switching). The entirety of the energy transfer in the U = 1/2 LI² formula is utilized.

SMPS design is a game of optimization. Correctly adjusting the inductance and current parameters ensures both the electrical safety of the system and eliminates heating/efficiency problems during the design phase. This energy formula, rooted in mathematical foundations, is a power electronics designer's closest friend.