Hidden behavior and characteristic analysis of passive components on PCB
Time:2022-07-08
Views:2019
Traditionally, EMC has been regarded as "black magic". In fact, EMC can be understood by mathematical formulas. However, even if there are mathematical analysis methods that can be used, those mathematical equations are still too complex for the actual EMC circuit design. Fortunately, in most practical work, engineers do not need to fully understand those complex mathematical formulas and the theoretical basis existing in EMC specifications. As long as they can understand how to meet EMC requirements through simple mathematical models.
Through simple mathematical formulas and electromagnetic theory, this paper explains the hidden behavior and characteristics of passive components on printed circuit boards (PCBs). These are the basic knowledge that engineers must have in advance when they want the designed electronic products to pass the EMC standard.
Wire and PCB routing
Wire, trace, fixed frame... And other seemingly insignificant components often become the best transmitter of RF energy (that is, the source of EMI). Each component has inductance, including the bond wire of silicon chip and the pins of resistance, capacitance and inductance. Each wire or route contains hidden parasitic capacitance and inductance. These parasitic components will affect the impedance of the wire and are very sensitive to frequency. According to the value of LC (determining the self resonance frequency) and the length of PCB wiring, self resonance can be generated between a component and PCB wiring, so an efficient radiation antenna is formed.
At low frequencies, the wire generally only has the characteristics of resistance. But at high frequency, the wire has the characteristics of inductance. Because when it becomes high frequency, it will cause the change of impedance, and then change the EMC design between conductor or PCB routing and grounding. At this time, ground plane and ground grid must be used.
The main difference between the wire and PCB routing is that the wire is circular and the routing is rectangular. The impedance of conductor or wiring includes resistance R and inductive reactance XL = 2 π fl. at high frequency, this impedance is defined as Z = R + J XL J2 π FL, and there is no capacitive reactance XC = 1/2 π FC. When the frequency is higher than 100 kHz, the inductive reactance is greater than the resistance. At this time, the conductor or wiring is no longer the connecting wire with low resistance, but the inductance. Generally speaking, the wire or wiring working above audio frequency should be regarded as inductance, not resistance, and can be RF antenna.
The length of most antennas is equal to 1/4 or 1/2 wavelength of a specific frequency（ λ）。 Therefore, in the EMC specification, it is not allowed for the conductor or wiring to operate at a certain frequency λ/ Work below 20, because it will suddenly become an efficient antenna. Inductance and capacitance will cause resonance of the circuit, which will not be recorded in their specifications.
For example, suppose there is a 10 cm wiring, r = 57 m Ω, 8 nh/cm, so the total inductance value is 80 NH. At 100 kHz, the inductive reactance of 50 m Ω can be obtained. When the frequency exceeds 100 kHz, this wiring will become inductance, and its resistance value can be ignored. Therefore, this 10 cm routing will form an efficient radiation antenna when the frequency exceeds 150 MHz. Because at 150 MHz, its wavelength λ= 2 meters, so λ/ 20 = 10 cm = length of wiring; If the frequency is greater than 150 MHz, its wavelength λ Will become smaller, 1/4 of it λ Or 1/2 λ The value will be close to the length of the cable (10 cm), so gradually form a perfect antenna.
resistance
Resistance is the most common component on PCB. The material of resistance (carbon synthesis, carbon film, mica, winding line, etc.) limits the effect of frequency response and EMC. Wound resistors are not suitable for high-frequency applications because there is too much inductance in the conductor. Although the carbon film resistor contains inductance, it is sometimes suitable for high-frequency applications because the inductance of its pin is not large.
What most people often ignore is the package size of the resistor and the parasitic capacitance. Parasitic capacitance exists between the two terminals of the resistor. They will damage the normal circuit characteristics at extremely high frequency, especially when the frequency reaches GHz. However, for most application circuits, the parasitic capacitance between the resistance pins is not more important than the pin inductance.
When the resistance bears the test of overvoltage stress, we must pay attention to the change of resistance. If "electrostatic discharge (ESD)" occurs on the resistance, something interesting will happen. If the resistance is a surface mount component, the resistance is likely to be punctured by the arc. If the resistance has a pin, ESD will find the high resistance (and high inductance) path of the resistance and avoid entering the circuit protected by the resistance. In fact, the real protector is the inductance and capacitance characteristics hidden in this resistance.
capacitance
Capacitors are generally used in the power bus to provide the functions of decoupling, bypassing, and maintaining a fixed DC voltage and current (bulk). A really simple capacitor will maintain its capacitance value until it reaches the self resonance frequency. Beyond this self resonance frequency, the capacitance characteristic will become like an inductance. This can be explained by the formula: xc=1/2 π FC, XC is the capacitive reactance (unit: Ω). For example: 10 μ F, at 10 kHz, the capacitive reactance is 1.6 Ω; At 100 MHz, it drops to 160 μ Ω。 Therefore, at 100 MHz, there is a short circuit effect, which is ideal for EMC. However, the electrical parameters of electrolytic capacitor: equivalent series inductance (ESL) and equivalent series resistance (ESR), will limit this capacitor to work below the frequency of 1 MHz.
The use of capacitance is also related to the pin inductance and volume structure. These factors determine the number and size of parasitic inductance. Parasitic inductance exists between the welding wires of the capacitor, which makes the capacitor behave like the inductance when it exceeds the self resonance frequency, so the capacitor loses its originally set function.
inductance
Inductance is used to control EMI in PCB. For inductance, its reactance is proportional to frequency. This can be explained by the formula: XL = 2 π FL, XL is inductive reactance (unit: Ω). For example, for an ideal 10 MH inductor, at 10 kHz, the inductive reactance is 628 Ω; At 100 MHz, it increases to 6.2 m Ω. Therefore, at 100 MHz, this inductance can be regarded as an open circuit. At 100 MHz, if a signal passes through the inductor, the signal quality will be degraded (this is observed from the time domain). Like the capacitance, the electrical parameters of the inductance (parasitic capacitance between coils) limit the inductance to work below the frequency of 1 MHz.
The question is, if inductors cannot be used at high frequencies, what should be used? The answer is, "ferite beads" should be used. Iron powder materials are iron magnesium or iron nickel alloys, which have high permeability. Under high frequency and high impedance, the capacitance between coils in the inductor will be the smallest. Iron powder beads are usually only suitable for high-frequency circuits, because at low frequencies, they basically retain the complete characteristics of inductance (including resistance and resistance components), which will cause some slight losses on the circuit. At high frequency, it basically has only the resistance component (J ω 50) And the resistance component will increase with the increase of frequency, as shown in Figure 1. In fact, iron powder beads are high-frequency attenuators of RF energy.
In fact, iron powder beads can be regarded as a resistor in parallel with an inductor. At low frequency, the resistance is "short circuited" by the inductance, and the current flows to the inductance; At high frequencies, the high reactance of the inductor forces the current to flow to the resistor.
In essence, iron powder beads are a "dissipative device", which converts high-frequency energy into heat energy. Therefore, in terms of efficiency, it can only be interpreted as resistance, not inductance.
transformer
The transformer usually exists in the power supply. In addition, it can be used to insulate data signals, i/o connections, and power supply interfaces. Depending on the type and application of the transformer, a shield may exist between the primary and secondary coils. The shield is connected to a grounded reference source to prevent capacitive coupling between the two sets of coils.
Transformers are also widely used to provide common mode (CM) insulation. These devices magnetically connect the primary coil and the secondary coil to transmit energy according to the differential mode (DM) signal at its input. As a result, the CM voltage passing through the primary coil will be rejected, so the purpose of common mode insulation is achieved. However, in the manufacture of transformers, there will be signal source capacitance between the primary and secondary coils. When the circuit frequency increases, the capacitive coupling ability will also be enhanced, which destroys the insulation effect of the circuit. If there is enough parasitic capacitance, high-frequency RF energy (from fast transients, ESD, lightning strikes, etc.) may pass through the transformer, causing the circuit at the other end of the insulation layer to also receive this instantaneous high voltage or high current.
The above has made a detailed description of the hidden characteristics of various passive components, and the following will explain why these hidden characteristics cause EMI in PCB.
On electromagnetic theory
The passive components mentioned above have hidden characteristics and generate RF energy in PCB, but why is this so? In order to understand the reason, we must understand Maxwell equation. Maxwell‘s four equations explain the relationship between electric field and magnetic field, and they are deduced from Ampere‘s law, Faraday‘s law, and Gauss‘ law. These equations describe the characteristics of electromagnetic field intensity and current density in a closed-loop environment, and need to be calculated using advanced calculus. Because Maxwell‘s equation is very complex, I will only make a brief description here. In fact, PCB wiring engineers do not need to fully understand the detailed knowledge of Maxwell equation. As long as they understand the key points, they can complete EMC design. The complete Maxwell equation is listed below:
In the above equation, J, e, B, h are vectors. In addition, the basic physical concepts related to Maxwell‘s equation are:
● Maxwell‘s equation describes the interaction between charge, current, magnetic field and electric field.
● Lorentz force can be used to describe the physical force exerted by electric and magnetic fields on charged particles.
● all substances have a composition relationship with other substances. This includes:
1. Conductivity: relationship between current and electric field (AUM‘s law of matter): J= σ E。
2. Magnetic conductivity: relationship between magnetic flux and magnetic field: B= μ H。
3. Dielectric constant: relationship between charge storage and an electric field: D= ε E。
J = conducted current density, a/m2
σ= Conductivity of substance
E = electric field strength, v/m
D = flux density, coulombs/ M2
ε= Vacuum permittivity, 8.85 pf/m
B = magnetic flux density, weber/ m2 or Tesla
H = magnetic field, a/m
μ= Magnetic conductivity of medium, h/m
According to Gauss‘ law, Maxwell‘s first equation is also called "divergence theorem". It can be used to explain the electrostatic field E generated due to the accumulation of charges. This phenomenon is best observed between two boundaries: conductive and non-conductive. According to Gauss‘ law, the behavior under boundary conditions will produce a conductive cage (also known as Faraday cage), which acts as a electrostatic shield. In a closed area surrounded by Faraday box, the electromagnetic waves around it cannot enter this area. If there is an electric field in Faraday box, the charge generated by this electric field is concentrated on the inside of the boundary at its boundary. The charge outside the boundary will be excluded by the internal electric field.
Maxwell‘s second equation indicates that in nature, there is no magnetic charge, only charge, that is, there is no single magnetic pole. Although the current grand unified theory predicts that there are few magnetic charges, it has not been proved by experiments so far. These charges are positively or negatively charged. The magnetic field is produced by the action of current and electric field. Due to the emission of current and electric field, they become the source of radiant energy. The magnetic field forms a closed cycle around the current, and the magnetic field is generated by the current.
Maxwell‘s third equation, also known as Faraday‘s law of induction, states that when a magnetic field surrounds a closed circuit, the magnetic field will cause the closed circuit to generate current. The third equation and the fourth equation are concomitant. The third equation shows that a changing magnetic field will produce an electric field. Magnetic fields usually exist in transformers or coils, such as motors, generators, etc. The interaction of the third and fourth equations is the main focus of EMC. Together, they illustrate how the coupled electric and magnetic fields radiate or propagate at the speed of light. This equation also explains the concept of "skin effect", which can predict the effectiveness of "magnetic shielding". In addition, it also explains the characteristics of inductance, which allows the antenna to exist reasonably.
Maxwell‘s fourth equation is also called Ampere‘s law. This equation describes two sources of magnetic field generation. The first source is that current flows in the form of transmitted charges. The second source is that when a variable electric field surrounds a closed circuit, a magnetic field will be generated. These sources of electricity and magnetism illustrate the role of inductance and electromagnetism. In this equation, J represents the component of magnetic field generated by current; It is the component of magnetic field generated by electric field.
In general, Maxwell equation can explain how EMI is generated in PCB. PCB is an environment that will change the current over time, and these calculus equations are to analyze the root cause of EMI. Electrostatic charge distribution produces electrostatic fields, not magnetic fields. Fixed current will produce static magnetic field and electrostatic field at the same time. Time varying current will generate electric and magnetic fields at the same time.
Electrostatic fields store energy, which is the basic function of capacitors: to accumulate and retain charge. Fixed current source is the basic function and concept of inductance.
Sources of electricity and magnetism
As mentioned earlier, the changing current will produce a magnetic field, and the electrostatic charge distribution will produce an electric field. The relationship between current and radiated electric field will be further discussed below. We must examine the structure of the current source and observe how it affects the radiation signal. In addition, we must also note that the signal strength will be lower when it is farther away from the current source.
Time varying current exists in two structures: 1 Source of magnetism (closed circuit), 2 Source of electricity (bipolar antenna). First, the source of magnetism is discussed.
Through simple mathematical formulas and electromagnetic theory, this paper explains the hidden behavior and characteristics of passive components on printed circuit boards (PCBs). These are the basic knowledge that engineers must have in advance when they want the designed electronic products to pass the EMC standard.
Wire and PCB routing
Wire, trace, fixed frame... And other seemingly insignificant components often become the best transmitter of RF energy (that is, the source of EMI). Each component has inductance, including the bond wire of silicon chip and the pins of resistance, capacitance and inductance. Each wire or route contains hidden parasitic capacitance and inductance. These parasitic components will affect the impedance of the wire and are very sensitive to frequency. According to the value of LC (determining the self resonance frequency) and the length of PCB wiring, self resonance can be generated between a component and PCB wiring, so an efficient radiation antenna is formed.
At low frequencies, the wire generally only has the characteristics of resistance. But at high frequency, the wire has the characteristics of inductance. Because when it becomes high frequency, it will cause the change of impedance, and then change the EMC design between conductor or PCB routing and grounding. At this time, ground plane and ground grid must be used.
The main difference between the wire and PCB routing is that the wire is circular and the routing is rectangular. The impedance of conductor or wiring includes resistance R and inductive reactance XL = 2 π fl. at high frequency, this impedance is defined as Z = R + J XL J2 π FL, and there is no capacitive reactance XC = 1/2 π FC. When the frequency is higher than 100 kHz, the inductive reactance is greater than the resistance. At this time, the conductor or wiring is no longer the connecting wire with low resistance, but the inductance. Generally speaking, the wire or wiring working above audio frequency should be regarded as inductance, not resistance, and can be RF antenna.
The length of most antennas is equal to 1/4 or 1/2 wavelength of a specific frequency（ λ）。 Therefore, in the EMC specification, it is not allowed for the conductor or wiring to operate at a certain frequency λ/ Work below 20, because it will suddenly become an efficient antenna. Inductance and capacitance will cause resonance of the circuit, which will not be recorded in their specifications.
For example, suppose there is a 10 cm wiring, r = 57 m Ω, 8 nh/cm, so the total inductance value is 80 NH. At 100 kHz, the inductive reactance of 50 m Ω can be obtained. When the frequency exceeds 100 kHz, this wiring will become inductance, and its resistance value can be ignored. Therefore, this 10 cm routing will form an efficient radiation antenna when the frequency exceeds 150 MHz. Because at 150 MHz, its wavelength λ= 2 meters, so λ/ 20 = 10 cm = length of wiring; If the frequency is greater than 150 MHz, its wavelength λ Will become smaller, 1/4 of it λ Or 1/2 λ The value will be close to the length of the cable (10 cm), so gradually form a perfect antenna.
resistance
Resistance is the most common component on PCB. The material of resistance (carbon synthesis, carbon film, mica, winding line, etc.) limits the effect of frequency response and EMC. Wound resistors are not suitable for high-frequency applications because there is too much inductance in the conductor. Although the carbon film resistor contains inductance, it is sometimes suitable for high-frequency applications because the inductance of its pin is not large.
What most people often ignore is the package size of the resistor and the parasitic capacitance. Parasitic capacitance exists between the two terminals of the resistor. They will damage the normal circuit characteristics at extremely high frequency, especially when the frequency reaches GHz. However, for most application circuits, the parasitic capacitance between the resistance pins is not more important than the pin inductance.
When the resistance bears the test of overvoltage stress, we must pay attention to the change of resistance. If "electrostatic discharge (ESD)" occurs on the resistance, something interesting will happen. If the resistance is a surface mount component, the resistance is likely to be punctured by the arc. If the resistance has a pin, ESD will find the high resistance (and high inductance) path of the resistance and avoid entering the circuit protected by the resistance. In fact, the real protector is the inductance and capacitance characteristics hidden in this resistance.
capacitance
Capacitors are generally used in the power bus to provide the functions of decoupling, bypassing, and maintaining a fixed DC voltage and current (bulk). A really simple capacitor will maintain its capacitance value until it reaches the self resonance frequency. Beyond this self resonance frequency, the capacitance characteristic will become like an inductance. This can be explained by the formula: xc=1/2 π FC, XC is the capacitive reactance (unit: Ω). For example: 10 μ F, at 10 kHz, the capacitive reactance is 1.6 Ω; At 100 MHz, it drops to 160 μ Ω。 Therefore, at 100 MHz, there is a short circuit effect, which is ideal for EMC. However, the electrical parameters of electrolytic capacitor: equivalent series inductance (ESL) and equivalent series resistance (ESR), will limit this capacitor to work below the frequency of 1 MHz.
The use of capacitance is also related to the pin inductance and volume structure. These factors determine the number and size of parasitic inductance. Parasitic inductance exists between the welding wires of the capacitor, which makes the capacitor behave like the inductance when it exceeds the self resonance frequency, so the capacitor loses its originally set function.
inductance
Inductance is used to control EMI in PCB. For inductance, its reactance is proportional to frequency. This can be explained by the formula: XL = 2 π FL, XL is inductive reactance (unit: Ω). For example, for an ideal 10 MH inductor, at 10 kHz, the inductive reactance is 628 Ω; At 100 MHz, it increases to 6.2 m Ω. Therefore, at 100 MHz, this inductance can be regarded as an open circuit. At 100 MHz, if a signal passes through the inductor, the signal quality will be degraded (this is observed from the time domain). Like the capacitance, the electrical parameters of the inductance (parasitic capacitance between coils) limit the inductance to work below the frequency of 1 MHz.
The question is, if inductors cannot be used at high frequencies, what should be used? The answer is, "ferite beads" should be used. Iron powder materials are iron magnesium or iron nickel alloys, which have high permeability. Under high frequency and high impedance, the capacitance between coils in the inductor will be the smallest. Iron powder beads are usually only suitable for high-frequency circuits, because at low frequencies, they basically retain the complete characteristics of inductance (including resistance and resistance components), which will cause some slight losses on the circuit. At high frequency, it basically has only the resistance component (J ω 50) And the resistance component will increase with the increase of frequency, as shown in Figure 1. In fact, iron powder beads are high-frequency attenuators of RF energy.
In fact, iron powder beads can be regarded as a resistor in parallel with an inductor. At low frequency, the resistance is "short circuited" by the inductance, and the current flows to the inductance; At high frequencies, the high reactance of the inductor forces the current to flow to the resistor.
In essence, iron powder beads are a "dissipative device", which converts high-frequency energy into heat energy. Therefore, in terms of efficiency, it can only be interpreted as resistance, not inductance.
transformer
The transformer usually exists in the power supply. In addition, it can be used to insulate data signals, i/o connections, and power supply interfaces. Depending on the type and application of the transformer, a shield may exist between the primary and secondary coils. The shield is connected to a grounded reference source to prevent capacitive coupling between the two sets of coils.
Transformers are also widely used to provide common mode (CM) insulation. These devices magnetically connect the primary coil and the secondary coil to transmit energy according to the differential mode (DM) signal at its input. As a result, the CM voltage passing through the primary coil will be rejected, so the purpose of common mode insulation is achieved. However, in the manufacture of transformers, there will be signal source capacitance between the primary and secondary coils. When the circuit frequency increases, the capacitive coupling ability will also be enhanced, which destroys the insulation effect of the circuit. If there is enough parasitic capacitance, high-frequency RF energy (from fast transients, ESD, lightning strikes, etc.) may pass through the transformer, causing the circuit at the other end of the insulation layer to also receive this instantaneous high voltage or high current.
The above has made a detailed description of the hidden characteristics of various passive components, and the following will explain why these hidden characteristics cause EMI in PCB.
On electromagnetic theory
The passive components mentioned above have hidden characteristics and generate RF energy in PCB, but why is this so? In order to understand the reason, we must understand Maxwell equation. Maxwell‘s four equations explain the relationship between electric field and magnetic field, and they are deduced from Ampere‘s law, Faraday‘s law, and Gauss‘ law. These equations describe the characteristics of electromagnetic field intensity and current density in a closed-loop environment, and need to be calculated using advanced calculus. Because Maxwell‘s equation is very complex, I will only make a brief description here. In fact, PCB wiring engineers do not need to fully understand the detailed knowledge of Maxwell equation. As long as they understand the key points, they can complete EMC design. The complete Maxwell equation is listed below:
In the above equation, J, e, B, h are vectors. In addition, the basic physical concepts related to Maxwell‘s equation are:
● Maxwell‘s equation describes the interaction between charge, current, magnetic field and electric field.
● Lorentz force can be used to describe the physical force exerted by electric and magnetic fields on charged particles.
● all substances have a composition relationship with other substances. This includes:
1. Conductivity: relationship between current and electric field (AUM‘s law of matter): J= σ E。
2. Magnetic conductivity: relationship between magnetic flux and magnetic field: B= μ H。
3. Dielectric constant: relationship between charge storage and an electric field: D= ε E。
J = conducted current density, a/m2
σ= Conductivity of substance
E = electric field strength, v/m
D = flux density, coulombs/ M2
ε= Vacuum permittivity, 8.85 pf/m
B = magnetic flux density, weber/ m2 or Tesla
H = magnetic field, a/m
μ= Magnetic conductivity of medium, h/m
According to Gauss‘ law, Maxwell‘s first equation is also called "divergence theorem". It can be used to explain the electrostatic field E generated due to the accumulation of charges. This phenomenon is best observed between two boundaries: conductive and non-conductive. According to Gauss‘ law, the behavior under boundary conditions will produce a conductive cage (also known as Faraday cage), which acts as a electrostatic shield. In a closed area surrounded by Faraday box, the electromagnetic waves around it cannot enter this area. If there is an electric field in Faraday box, the charge generated by this electric field is concentrated on the inside of the boundary at its boundary. The charge outside the boundary will be excluded by the internal electric field.
Maxwell‘s second equation indicates that in nature, there is no magnetic charge, only charge, that is, there is no single magnetic pole. Although the current grand unified theory predicts that there are few magnetic charges, it has not been proved by experiments so far. These charges are positively or negatively charged. The magnetic field is produced by the action of current and electric field. Due to the emission of current and electric field, they become the source of radiant energy. The magnetic field forms a closed cycle around the current, and the magnetic field is generated by the current.
Maxwell‘s third equation, also known as Faraday‘s law of induction, states that when a magnetic field surrounds a closed circuit, the magnetic field will cause the closed circuit to generate current. The third equation and the fourth equation are concomitant. The third equation shows that a changing magnetic field will produce an electric field. Magnetic fields usually exist in transformers or coils, such as motors, generators, etc. The interaction of the third and fourth equations is the main focus of EMC. Together, they illustrate how the coupled electric and magnetic fields radiate or propagate at the speed of light. This equation also explains the concept of "skin effect", which can predict the effectiveness of "magnetic shielding". In addition, it also explains the characteristics of inductance, which allows the antenna to exist reasonably.
Maxwell‘s fourth equation is also called Ampere‘s law. This equation describes two sources of magnetic field generation. The first source is that current flows in the form of transmitted charges. The second source is that when a variable electric field surrounds a closed circuit, a magnetic field will be generated. These sources of electricity and magnetism illustrate the role of inductance and electromagnetism. In this equation, J represents the component of magnetic field generated by current; It is the component of magnetic field generated by electric field.
In general, Maxwell equation can explain how EMI is generated in PCB. PCB is an environment that will change the current over time, and these calculus equations are to analyze the root cause of EMI. Electrostatic charge distribution produces electrostatic fields, not magnetic fields. Fixed current will produce static magnetic field and electrostatic field at the same time. Time varying current will generate electric and magnetic fields at the same time.
Electrostatic fields store energy, which is the basic function of capacitors: to accumulate and retain charge. Fixed current source is the basic function and concept of inductance.
Sources of electricity and magnetism
As mentioned earlier, the changing current will produce a magnetic field, and the electrostatic charge distribution will produce an electric field. The relationship between current and radiated electric field will be further discussed below. We must examine the structure of the current source and observe how it affects the radiation signal. In addition, we must also note that the signal strength will be lower when it is farther away from the current source.
Time varying current exists in two structures: 1 Source of magnetism (closed circuit), 2 Source of electricity (bipolar antenna). First, the source of magnetism is discussed.
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