Since power MOS was widely used in switching power supplies, the Miller effect has gradually been valued by power application engineers. Most novice electronic engineers feel that the Miller effect is a new discovery. In fact, the Miller effect was discovered very early, not only earlier than MOS tubes, but even much earlier than BJT (bipolar transistor). From 1919 to 1920, American radio engineer John Milton Miller discovered this effect, which was later named after his surname, while studying vacuum tubes. You should know that the world's first industrial vacuum tube company, the American Radio Corporation, was established in 1919 with investment from four companies including General Electric, and it did not start producing vacuum tubes until 1920. Before that, vacuum tubes were all made one by one by hand in the laboratory. So we say that the discovery of the Miller effect is really quite early. The Miller effect has a great influence on the performance of high-frequency amplifiers. It is precisely because engineers tried every means to eliminate the influence of the Miller effect of triode vacuum tubes that electronic engineers invented quadrupole vacuum tubes and quintuple vacuum tubes after triode vacuum tubes, which further improved the performance of vacuum tube high-frequency amplification and gained wider application. To explain what the Miller effect is, please look at Figure (01) first.
Figure (01) This is a simulation diagram. The circuit is very simple, with only a signal source V1 and a capacitor C1, and a multimeter to measure current. If we do not know the capacitance of the capacitor C1, we can also calculate the capacitive reactance of the capacitor C1 from the current measured by the ammeter and the voltage across the signal source V1, and further calculate the capacitance from the frequency and capacitive reactance of the signal source V1. What will happen if a DC power supply is connected to the circuit? Please see the simulation results in Figure (02).
Figure (02) The value displayed by the ammeter in Figure (02) is the same as that in Figure (01). This is also expected. For AC signals, the internal resistance of a DC voltage source is zero, which is equivalent to a short circuit. However, a capacitor cannot pass DC. The output amplitude and frequency of the AC signal source do not change, and of course the current passing through the capacitor does not change. However, if the DC power supply is replaced with an AC power supply V2 with the same frequency but opposite phase as the signal source V1, the situation becomes very different. See Figure (03).
Figure (03) In Figure (03), the DC power supply is changed to an AC power supply with the same frequency but opposite phase as V1, and its amplitude is 50 times that of V1. Please note: V2 and V1 are in opposite phase with respect to the ground. We can see that the current flowing through the capacitor changes from 1.125mA to 57.375mA. This is easy to explain. The two power supplies are in opposite phases with respect to the ground, but they are in the same phase in series with respect to the capacitor. In other words, the voltage across the capacitor changes from the original 1V peak to 51V peak (25kHz). Other conditions remain unchanged. Of course, the current flowing through the capacitor should increase to 51 times the original. Check: 1.125mA multiplied by 51 is indeed 57.375mA. 1.125mA is the contribution of V1, and the other 56.25mA is the contribution of V2. How does this phenomenon occur? In fact, it is also very simple: the right end of capacitor C1 is grounded or connected to a fixed DC voltage. When the voltage across power supply V1 rises by ΔV, the voltage at the right end of the capacitor does not change. When the right end of the capacitor is connected to power supply V2 with the opposite phase to V1, the voltage across power supply V1 rises by ΔV, but the voltage at the right end of the capacitor drops by KΔV, where K is the ratio of the output amplitude of power supply V2 to the output amplitude of power supply V1 (absolute value, 50 in Figure (03)). Of course, the current flowing through the capacitor is K+1 times the current flowing through the capacitor when the right end of the capacitor is grounded or connected to a fixed DC power supply. However, if we do not know that V2 has been replaced by a 12V DC power supply with a 25kHz frequency, a peak value of 50V, and an AC power supply with a phase opposite to that of V1, we will think that the capacitance of capacitor C1 is 510nF, because according to the 25kHz/1V and 57.375mA, the calculated capacitance of C1 is exactly 510nF. In other words, it seems that the capacitance of capacitor C1 has increased by 51 times. Although the Miller effect was first discovered in the study of the operation of vacuum tubes, vacuum tubes are rarely used in modern times, and vacuum tubes are basically not mentioned in analog circuit textbooks, so we use the more common bipolar transistor as an example.
Figure (04) Figure (04) is a fairly typical bipolar transistor common emitter amplifier circuit, which is very common in practical electronic circuits. The amplifier composed of triodes in the figure, point A is the signal input end, and point B is the signal output end. For the capacitance Cbc between the base and collector of triode Q1 (including the PN junction capacitance and the distributed capacitance between the leads), point A is equivalent to the left end of capacitor C1 in Figure (03), and point B is equivalent to the right end of capacitor C1 in Figure (03). See Figure (05). This is because, for the distributed capacitance Cbc between the base and collector of the transistor, its left end is the input signal V1, and its right end is amplified by K times (K is the voltage amplification factor of the amplifier circuit at this stage, the absolute value), and the amplified signal at point B is exactly inverse to the signal at point A, which is equivalent to the power supply V2 in Figure (03).
Figure (05) Obviously, looking from the signal source to the right, the current provided by the signal source is increased to K+1 times compared to when there is no amplification (for example, the collector load resistor R2 is short-circuited), of which 1 times is generated by the signal source V1 when the transistor collector is AC grounded, and K times is generated by the inverted AC voltage output by the amplifier after the collector is connected to the load to become an inverting amplifier. If we abstract the specific transistor common emitter amplifier circuit shown in Figure (05) into the amplifier circuit shown in Figure (06), the Miller effect still exists. In Figure (06), Rs is the internal resistance of the signal source, the voltage gain of the inverting amplifier is K (absolute value), and the capacitor Cc connected from the output end to the inverting input end is equivalent to the capacitor Cbc in Figure (05). We can see that when the potential at the left end of the capacitor Cc changes by ΔV, the potential at the right end changes by KΔV, and the change direction is opposite. From this, we can know that the current flowing through the capacitor Cc must be K+1 times when the right end of the capacitor Cc is grounded. Looking to the right from the ZIN mark in the figure, because the current flowing through the capacitor when it is connected to the output end of the inverting amplifier is K+1 times larger than when the right end of the capacitor is grounded, it is obvious that when the capacitor is connected to the output end of the amplifier, the input impedance of the amplifier is relatively small for the signal source.
Figure (06) For the signal source, the capacitor Cc connected to the output end of the amplifier is the same as a capacitor C
M with a capacity of (K+1)Cc and grounded, because the current flowing through the signal source is the same in both cases. For the output of the amplifier, the current flowing through the capacitor Cc is equivalent to being grounded through a capacitor Co from the output. If the voltage gain of the amplifier is infinite, then the capacitance of Co is equal to that of Cc. However, the actual voltage gain of the amplifier is only K times (absolute value), so the capacitance of the equivalent capacitor Co and Cc are not equal. However, the K value is usually large (much greater than 1), so the value of Co is not much different from that of Cc. Considering that the output capability of the amplifier is relatively strong, Co has little effect on the operation of the amplifier. The equivalent capacitor C
M at the input and the internal resistance R
S of the signal source form a first-order low-pass filter circuit. Obviously, when the frequency of the signal source is relatively high, the effect on the operation of the amplifier is relatively large, which is manifested by the effect on the output of the signal source.
Figure (07) We have seen that the common emitter amplifier circuit of the bipolar transistor (BJT) has the Miller effect. So, does the field effect transistor (FET, including junction type and MOS type field effect transistor) also have the Miller effect? The output of the common source field effect transistor amplifier circuit is inversely proportional to the input, and of course the Miller effect will also be exhibited.
Figure (08) Figure (08) is a typical common source output characteristic curve family of the enhanced power MOS tube IRF840, which is taken from the manual of this model of MOS tube. The bottom curve in the figure is the relationship curve between the drain voltage VDS and the drain current ID when the gate voltage V
GS is 4V. Below this curve, the MOS tube is not turned on. In the analog circuit textbook, it is called the cut-off region. Of course, the MOS tube does not conduct and has no amplification effect. After the gate voltage exceeds 4V, the drain current rises rapidly with the gate voltage. This part is called the saturation region in the analog circuit textbook. This is the region where the MOS tube has an amplification effect. The curves of the leftmost curve family are almost combined into one. This part is called the variable resistance region in the analog circuit textbook. The MOS tube also has no amplification effect in this region. Pay attention to the names of the cut-off region, saturation region and variable resistance region, and do not confuse them with the three regions of the bipolar transistor.
Figure (09) Figure (09) is the characteristic curve of the gate charge and discharge amount and the gate-to-source voltage of the MOS tube (IRF840) of Figure (08). It can be seen that the curve is basically composed of three straight lines: from the origin to point A in the figure, from point A to point B in the figure, and the part to the right of point B in the figure. Let's see what this curve means. In this curve, the horizontal axis is the gate charge amount and the vertical axis is the gate voltage. Then the slope of the curve is the ratio of the gate voltage increment to the gate charge increment (ΔV/ΔQ). The inverse of the slope is ΔQ/ΔV, which is exactly the capacitance! The inverse of the slope is the capacitance, which means that the capacitance is smaller where the slope is larger (more "steep"), such as the section from the origin to point A, and the capacitance is larger where the slope is smaller (close to "horizontal"), such as the section from point A to point B. Then, why is the gate charge and discharge charge and gate-to-source voltage characteristic curve in Figure (09) so clearly divided into three sections? These three sections correspond exactly to the three regions of the MOS tube output characteristic curve family in Figure (08): cut-off region, saturation region and variable resistance region. We know that in Figure (08), the gate voltage starts to rise from zero. Before the gate voltage reaches the turn-on voltage, there is no drain current in the MOS tube, and of course there is no amplification effect. In the cut-off region of the MOS tube, as the gate voltage starts to rise from zero, the signal source charges the distributed capacitance between the gate and the source and the distributed capacitance between the gate and the drain. This is the curve from the origin to point A in Figure (09). The curve is very close to a straight line and corresponds to the cut-off region in Figure (08). After the gate voltage reaches the turn-on voltage, the MOS tube begins to conduct and enters the saturation region. The MOS tube begins to have an amplification effect. Since the output and input of the common source amplifier circuit are inverted, we judge that the Miller effect must occur. The Miller effect of MOS tube is to increase the distributed capacitance between the gate and the drain to K+1 times (K is the absolute value of the voltage amplification factor). Because K is usually relatively large, at least ten times, and up to a hundred times, the equivalent capacitance is also relatively large. As we said before: the relatively large capacitance is represented by a line with a small slope close to the horizontal direction in Figure (09). This is exactly the section from point A to point B in Figure (09). The curve from point A to point B becomes close to horizontal precisely because of the Miller effect. The right part of point B in Figure (09) corresponds to the variable resistance area in Figure (08). In this area, the MOS tube has no amplification effect, and there is no Miller effect, so the curve becomes steeper (the slope becomes larger). However, the slope of the right part of point B is smaller than the slope of the part from the origin to point A, because the conductive channel of the field effect tube has been opened. Figure (10) is a schematic diagram of MOSFET, which is excerpted from "Basics of Electronic Technology"Analog Part》Kang Huaguang, 5th edition.
Figure (10) In Figure (10), the structure of the MOS tube is clearly marked, especially the conductive channel. The conductive channel is insulated in the cut-off region of the MOS tube output characteristic curve family, but has a very small resistance in the variable resistance region and can be considered as a conductor. Obviously, the distributed capacitance between the gate (marked as the gate in the figure) and the source and drain changes with the change of the conductive channel resistance. The distributed capacitance in the variable resistance region of the MOS tube is much larger than that in the cut-off region of the MOS tube. Therefore, the slope of the right part of point B in Figure (09) is smaller than the slope of the part from the origin to point A. The structure of the power MOS tube currently widely used in switching power supplies is different from that shown in Figure (10), but the working principle is the same. The distributed capacitance of the gate to the conductive channel still follows the rule that the MOS tube is larger when it is turned on than when it is turned off. From the fact that the slope of the curve from point A to point B in Figure (09) is much smaller than the slope of the curve from the origin to point A, it can be seen that the influence of the Miller effect is very large. The Miller effect increases the apparent input capacitance to K+1 times. If the MOS tube is used as a linear amplifier, such as an audio power amplifier, then the signal source internal resistance and the equivalent input capacitance generated by the Miller effect constitute a first-order low-pass filter, as shown by RS and CM in Figure (07). This low-pass filter will cause the input signal to be attenuated in the high frequency band. If the signal source internal resistance is slightly larger, the amplifier formed by the tube will even have a reduced amplitude-frequency characteristic in the high audio band (10kHz or even lower), and it is obviously impossible to form a broadband power amplifier. The influence of the Miller effect is smaller for bipolar transistors than for MOSFET tubes. This is because the input resistance of bipolar transistors is relatively small (so-called current drive), and a low internal resistance signal source is required to drive it. In Figure (07), the equivalent capacitance C
M generated by the Miller effect is relatively large compared to the input resistance, so the influence of the Miller effect is not significant. If the MOSFET works in a switching state, such as for a switching power supply, it can be seen from Figure (10) that if the signal amplitude driving the MOS tube is from zero to 10V (red dotted line), then the total charge amount charged (or discharged) to the gate of the MOS tube each time is 41.5nC, of which the charge amount charged due to the Miller effect is 22.5nC (from point A to point B), accounting for a little more than half of the total charge amount. This will of course increase the burden on the drive circuit, affect the rise and fall time of the switch tube current, and increase the loss of the switch tube when the operating frequency of the switching power supply is relatively high.
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