1. Resistance
Resistor equivalent circuit
Figure 1. Resistor equivalent circuit
Equivalent impedance of resistor
The resistance value measured for the same resistive element is different when it is subjected to DC and AC current. Under high-frequency AC, the effects of the lead inductance L0 and distributed capacitance C0 of the resistive element must be considered. Its equivalent circuit is shown in Figure 1, where R is an ideal resistor. From the figure, it can be seen that the equivalent impedance of this element at frequency f is...
In the above formula, ω＝2πf, Re and Xe are the equivalent resistance component and reactance component, respectively, and
Formula 2
From the above formula, it can be seen that Re depends not only on f, but also on L0 and C0. This indicates that when L0 and C0 are not negligible, measuring the resistance of this resistive element under AC conditions will yield Re, not R.
2. Inductance
Inductor equivalent circuit
Figure 2. Equivalent circuit of inductor
Equivalent impedance of inductor
In addition to the inductance L, an inductor always has a loss resistance RL and a distributed capacitance CL. Generally, the effects of RL and CL are negligible. When an inductor is connected to DC and reaches steady state, it can be considered a resistor; if connected to a low-frequency AC circuit, it can be considered as a series connection of an ideal inductance L and a loss resistance RL; at high frequencies, its equivalent circuit is shown in Figure 2. Comparing Figure 1 and Figure 2, it can be seen that they are essentially the same. The high-frequency equivalent impedance of the inductor can be determined with reference to Equation 1.
Formula 3
In the formula, Re and Le are the equivalent resistance and equivalent inductance of the inductive element, respectively.
From the above formula, we know that Le will be equal to or close to L only when CL is very small or when RL, CL and ω are not large.
3. Capacitor
Capacitor Equivalent Circuit
Figure 3. Capacitor equivalent circuit
Equivalent impedance of capacitor
Under alternating current, a capacitor always has a certain dielectric loss. In addition, its leads have a certain resistance Rn and a distributed inductance Ln. Therefore, the equivalent circuit of a capacitor is shown in Figure 3. In the figure, C is the inherent capacitance of the component, and Rc is the equivalent resistance due to dielectric loss. The equivalent impedance is...
Formula 4
In the formula, Re and Ce are the equivalent resistance and equivalent capacitance of the capacitor element, respectively. Since the dielectric loss is generally very small and negligible (i.e., Rc→∞), Ce can be expressed as...
Formula 5
As can be seen from the above discussion, when measuring R, L, and C under AC conditions, what is actually measured are the equivalent values Re, Le, and Ce. Since the actual impedance of resistors, capacitors, and inductors varies with the environment and operating frequency, impedance measurements should be performed as close as possible to the actual operating conditions (especially the operating frequency). Otherwise, the measured results will have a large error, or even be incorrect.
4. Diode
Forward conduction equivalent circuit of a power diode
(1): Equivalent circuit
(2): Explanation:
When a diode is forward-biased, it can be represented by an equivalent voltage drop. This voltage is related to temperature and the current flowing through it; as temperature increases, the voltage decreases; as current increases, the voltage increases. Detailed relationship curves can be obtained from the manufacturer's datasheet.
Reverse cutoff equivalent circuit of a power diode
(1): Equivalent circuit
(2): Explanation:
When a diode is reverse-biased, it can be equivalent to a capacitor. Its capacitance depends on the applied reverse voltage, ambient temperature, etc., and its value can be obtained from the manufacturer's manual.
Summary of steady-state characteristics of power diodes
(1): Current/voltage curve of power diode in steady state
(2): Explanation:
The steady-state operating point of a diode during forward conduction:
When Vin >> Vd, we have:
The range of Vd for different diodes is 0.35V to 2V.
The steady-state operating point of the diode when it is reverse cutoff is: Id≈0, Vd=-Vin
(3): Summary of steady-state characteristics:
--It is a unidirectional conductive device (without forward blocking capability).
--It is an uncontrollable device, and its on/off state is controlled by the polarity of its two voltages, without any other external control;
--Ordinary diodes have a large power capacity, but a very low frequency;
--There are three types of switching diodes, each with different steady-state and switching characteristics:
--Fast recovery diode;
--Ultra-fast recovery, soft recovery diode;
--Schottky diode (reverse blocking voltage drop << 200V, no reverse recovery problem);
--The forward current rating of a device is indicated by its average value; as long as the actual average current does not exceed its rated value and heat dissipation is not a problem, the device is safe.
--The on-state voltage of the device has a negative temperature coefficient, therefore it cannot be directly connected in parallel;
--Current SiC power diode devices have excellent reverse recovery characteristics.
5. MOSFET
Forward conduction equivalent circuit of power MOSFET
(1): Equivalent circuit
(2): Explanation:
When a power MOSFET is forward-biased, it can be represented by an equivalent resistor. This resistance is temperature-dependent; as the temperature increases, the resistance increases. It is also related to the gate drive voltage; as the drive voltage increases, the resistance decreases. Detailed relationship curves can be obtained from the manufacturer's datasheet.
Reverse conduction equivalent circuit of power MOSFET (1)
(1): Equivalent circuit (gate uncontrolled)
(2): Explanation:
The equivalent circuit of the internal diode can be represented by a voltage drop. This diode is the body diode of the MOSFET. In most cases, it should be avoided because of its poor characteristics.
Reverse conduction equivalent circuit of power MOSFET (2)
(1): Equivalent circuit (gate plus control)
(2): Explanation:
The reverse conduction of a power MOSFET under gate-level control can also be represented by an equivalent resistor. This resistance is temperature-dependent; as temperature increases, the resistance increases. It is also related to the gate drive voltage; as the drive voltage increases, the resistance decreases. Detailed relationship curves can be obtained from the manufacturer's datasheet. This operating state is called synchronous rectification operation of the MOSFET, and it is a very important operating state in low-voltage, high-current output switching power supplies.
Equivalent circuit of forward cutoff of power MOSFET
(1): Equivalent circuit
(2): Explanation:
When a power MOSFET is forward-biased, it can be equivalent to a capacitor. Its capacitance depends on the applied forward voltage, ambient temperature, etc., and its value can be obtained from the manufacturer's manual.
Summary of steady-state characteristics of power MOSFETs
(1): Current/voltage curves of power MOSFET in steady state
(2): Explanation:
Steady-state operating point of a power MOSFET during forward saturation conduction:
When the gate is not controlled, its reverse conduction steady-state operating point is the same as that of a diode.
(3): Summary of steady-state characteristics:
--The voltage Vgs between the gate and source controls the conduction state of the device; when Vgs > Vth, the device is in the conduction state; the on-state resistance of the device is related to Vgs, the larger Vgs, the smaller the on-state resistance; most devices have a Vgs of 12V-15V, and a rated value of ±30V.
--The drain current rating of a device is indicated by its effective value or average value; as long as the actual effective value of the drain current does not exceed its rated value and heat dissipation is not a problem, the device is safe.
--The on-state resistance of the device has a positive temperature coefficient, so in principle it is easy to connect in parallel to expand the capacity. However, when connecting in parallel, the symmetry of the drive and the dynamic current sharing problem must be considered.
--Currently, logic-level power MOSFETs only require 5V Vgs to ensure very low drain-source on-state resistance;
--The synchronous rectification operation of the device has become increasingly widespread because its on-state resistance is very small (currently the smallest is 2-4 milliohms), making it the most critical device in low-voltage, high-current output DC/DC converters.
Equivalent circuit of power MOSFET including parasitic parameters
(1): Equivalent circuit
(2): Explanation:
A practical power MOSFET can be equivalent to three junction capacitances, three channel resistances, an internal diode, and an ideal MOSFET. The three junction capacitances are all related to the junction voltage, while the gate channel resistance is generally very small. The sum of the two channel resistances of the drain and source is the on-state resistance of the MOSFET when it is saturated.
