**1. Electrical parameters of electrolytic capacitors**

The electrolytic capacitors here mainly refer to aluminum electrolytic capacitors, and their basic electrical parameters include the following five points:

1) Capacitance value

The capacitance of an electrolytic capacitor depends on the impedance it exhibits when operating under alternating voltage. Therefore, the capacitance value, also known as the AC capacitance value, varies with changes in operating frequency, voltage, and measurement methods.

According to the standard JISC 5102, the measurement conditions for the capacitance of aluminum electrolytic capacitors are at a frequency of 120Hz, a maximum AC voltage of 0.5Vrms, and a DC bias voltage of 1.5-2.0V. It can be asserted that the capacity of aluminum electrolytic capacitors decreases with increasing frequency.

2) Tangent value of loss angle Tan δ

In the equivalent circuit of a capacitor, the ratio of the series equivalent resistance ESR to the capacitance 1/ω C is called Tan δ, where ESR is calculated at 120Hz.

Obviously, Tan δ increases with the increase of measurement frequency and decreases with the decrease of measurement temperature.

3) Impedance Z

The resistance that obstructs the passage of alternating current at a specific frequency is called impedance (Z). It is closely related to the capacitance and inductance values in the equivalent circuit of capacitors, and is also related to ESR.

Z = √ [ESR2 + (XL - XC)2 ]

In the formula, XC=1/ω C=1/2 π fC

XL = ωL = 2πfL

The capacitance reactance (XC) of a capacitor gradually decreases with increasing frequency in the low frequency range, and when the frequency continues to increase and reaches the mid frequency range, the reactance (XL) drops to the value of ESR.

When the frequency reaches the high frequency range, the inductive impedance (XL) becomes dominant, so the impedance increases with the increase of frequency.

4) Leakage current

The dielectric of capacitors has a significant hindering effect on direct current. However, due to the presence of electrolyte on the aluminum oxide film dielectric, a small current called leakage current is generated during the re formation and repair of the oxide film when voltage is applied. Usually, leakage current increases with temperature and voltage.

5) Ripple current and ripple voltage

In some sources, these two are referred to as "ripple current" and "ripple voltage", which are actually ripple current and ripple voltage. The meaning is the ripple current/voltage value that a capacitor can withstand. Their relationship with ESR is closely related and can be expressed by the following equation:

Urms = Irms × R

In the equation, Vrms represents ripple voltage

Irms represents ripple current

R represents the ESR of the capacitor

As can be seen from the above, when the ripple current increases, even with the ESR remaining constant, the ripple voltage will increase exponentially. In other words, as the ripple voltage increases, the ripple current also increases, which is why capacitors are required to have lower ESR values.

After adding ripple current, the equivalent series resistance (ESR) inside the capacitor causes heating, which affects the service life of the capacitor. Generally, ripple current is proportional to frequency, so ripple current is also relatively low at low frequencies.

**9. Basic formula for capacitor parameters**

1) Capacity (Farads)

Imperial system: C=(0.224 × K · A)/TD

Metric system: C=(0.0884 × K · A)/TD

2) Energy stored in capacitors

1/2CV2

3) Linear charging capacity of capacitors

I = C (dV/dt)

Z = √ [ RS2 + (XC – XL)2 ]

XC= 1/(2πfC)

D. F.=tan δ (loss angle)

= ESR / XC

= (2πfC)(ESR)

Q = cotan δ = 1/ DF

ESR = (DF) XC = DF/ 2πfC

Power Loss = (2πfCV2 ) (DF)

PF=sin δ (loss angle) - cos Φ (phase angle)

rms = 0.707 × Vp

KVA = 2πfCV2 × 10-3

T.C. = [ (Ct – C25) / C25 (Tt – 25) ] × 106

CD = [ (C1 – C2) / C1 ] × 100

L0 / Lt = (Vt / V0)X (Tt / T0)Y

N capacitors in series: 1/CT=1/C1+1/C2++ 1/Cn

Two capacitors in series: CT=C1 · C2/(C1+C2)

CT = C1 + C2 + …. + Cn

A.R. = % ?C / decade of time

K=dielectric constant;

A=Area;

TD=insulation layer thickness;

V=Voltage;

RS=series resistance;

F=frequency;

L=inductance coefficient;

δ=loss angle;

Ø=phase angle;

L0=service life;

Lt=test life;

Vt=test voltage;

V0=working voltage;

Tt=test temperature;

T0=working temperature;

X, Y=the effect index of voltage and temperature.

4) Total impedance of capacitor (ohms)

Z=√ [RS2+(XC-XL) 2]

5) Capacitive reactance (ohms)

XC=1/(2 π fC)

6) Phase angle Φ

Ideal capacitor: 90% ahead of the current voltage?

Ideal inductor: lagging the current voltage by 90?

Ideal resistor: in phase with the current voltage

7) Dissipation coefficient (%)

D. F.=tan δ (loss angle)

= ESR / XC

= (2πfC)(ESR)

8) Quality factors

Q = cotan δ = 1/ DF

9) Equivalent series resistance ESR (ohms)

ESR = (DF) XC = DF/ 2πfC

10) Power consumption

Power Loss = (2πfCV2 ) (DF)

11) Power factor

PF=sin δ (loss angle) - cos Φ (phase angle)

12) Root Mean Square

rms = 0.707 × Vp

13) Kilovolt ampere KVA (kilowatts)

KVA = 2πfCV2 × 10-3

14) Temperature coefficient of capacitors

T.C. = [ (Ct – C25) / C25 (Tt – 25) ] × 106

15) Capacity loss (%)

CD = [ (C1 – C2) / C1 ] × 100

16) Reliability of Ceramic Capacitors

L0 / Lt = (Vt / V0)X (Tt / T0)Y

17) Capacity value when connected in series

N capacitors in series: 1/CT=1/C1+1/C2++ 1/Cn

Two capacitors in series: CT=C1 · C2/(C1+C2)

18) Capacity value during parallel connection

CT = C1 + C2 + …. + Cn

19) Repetition rate

A.R. = % ?C / decade of time

The symbols in the above formula are explained as follows:

K=dielectric constant;

A=Area;

TD=insulation layer thickness;

V=Voltage;

RS=series resistance;

F=frequency;

L=inductance coefficient;

δ=loss angle;

Ø=phase angle;

L0=service life;

Lt=test life;

Vt=test voltage;

V0=working voltage;

Tt=test temperature;

T0=working temperature;

X, Y=the effect index of voltage and temperature.

**10. X and Y safety capacitors at the power input end**

At the input end of the AC power supply, it is generally necessary to add three capacitors to suppress EMI conducted interference. The input of AC power supply can generally be divided into three wires: live wire (L)/neutral wire (N)/ground wire (G). The capacitors connected in parallel between the live wire and the ground wire, as well as between the neutral wire and the ground wire, are generally referred to as Y capacitors.

The connection position of these two Y capacitors is crucial and must comply with relevant safety standards to prevent electronic device leakage or shell electrification, which can easily endanger personal safety and life. Therefore, they are both safety capacitors, and the capacitance value must not be too large, and the withstand voltage must be high.

Generally, machines working in subtropical regions are required to have a ground leakage current not exceeding 0.7mA; Working on temperate machines, it is required that the ground leakage current should not exceed 0.35mA. Therefore, the total capacity of Y capacitors generally cannot exceed 4700pF.

Hardware Notebook "special reminder: Y capacitor is a safety capacitor and must obtain certification from a safety testing agency. The withstand voltage of Y capacitors is generally marked with safety certification marks and the words AC250V or AC275V, but their true DC withstand voltage is as high as 5000V or above. Therefore, Y capacitors cannot be replaced with ordinary capacitors with nominal withstand voltage of AC250V or DC400V at will.

The capacitor connected in parallel between the live and neutral suppression lines is generally referred to as an X capacitor. Due to the critical location of the capacitor connection, it also needs to comply with safety standards.

Therefore, X capacitor is also one of the safety capacitors. The capacitance of the X capacitor is allowed to be larger than that of the Y capacitor, but a safety resistor must be connected in parallel at both ends of the X capacitor to prevent the power cord plug from being charged for a long time due to the charging and discharging process of the capacitor when unplugging or unplugging the power cord.

According to safety standards, when the power cord of a working machine is unplugged, the voltage (or ground potential) at both ends of the power cord plug must be less than 30% of the original rated working voltage within two seconds.

Similarly, X capacitor is also a safety capacitor and must obtain certification from a safety testing agency. The withstand voltage of X capacitors is generally marked with safety certification marks and the words AC250V or AC275V, but their true DC withstand voltage can reach 2000V or more. When using them, do not use ordinary capacitors with nominal withstand voltage AC250V or DC400V as substitutes.

X capacitors are generally made of polyester film capacitors with high ripple current. These capacitors have a large volume, but they also allow for a large current for instantaneous charging and discharging, while their internal resistance is relatively small.

The indicators of ripple current in ordinary capacitors are very low, and the dynamic internal resistance is high. Replacing the X capacitor with a regular capacitor not only fails to meet the voltage resistance requirements, but also makes it difficult to meet the general ripple current indicators.

In fact, it is unlikely to completely filter out conducted interference signals solely relying on Y and X capacitors. Because the spectrum of interference signals is very wide, covering a frequency range of tens of KHz to hundreds of MHz, and even thousands of MHz.

Usually, filtering out low-end interference signals requires a large capacity filtering capacitor, but due to safety constraints, the capacity of Y and X capacitors cannot be used too large; The filtering performance of high-capacity capacitors for high-end interference signals is extremely poor, especially the high-frequency performance of polyester film capacitors is generally poor.

Because it is produced using winding technology and the high-frequency response characteristics of polyester film dielectric are far different from those of ceramics or mica, generally polyester film dielectric has adsorption effect, which will reduce the operating frequency of capacitors. The operating frequency range of polyester film capacitors is about 1MHz, and the impedance will significantly increase beyond 1MHz.

Therefore, in order to suppress the conducted interference generated by electronic devices, in addition to using Y capacitors and X capacitors, multiple types of inductive filters should also be selected simultaneously and combined to filter out interference.

Inductive filters mostly belong to low-pass filters, but there are also many specifications and types of inductive filters, such as differential mode, common mode, as well as high frequency, low frequency, etc. Each type of inductor mainly works to filter out interference signals at a certain small frequency, and has little effect on filtering out interference signals at other frequencies.

Usually, inductors with high inductance have a large number of coil turns, resulting in a large distributed capacitance of the inductor. High frequency interference signals will be bypassed through distributed capacitors. Moreover, magnetic cores with high magnetic permeability have lower operating frequencies.

At present, the operating frequency of the widely used inductor filter cores is mostly below 75MHz. For occasions with high working frequency requirements, high-frequency ring magnetic cores must be selected. High frequency ring magnetic cores generally have low magnetic permeability but very low leakage inductance, such as amorphous alloy magnetic cores, Permalloy, etc.

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