1 Basic knowledge 1.1 Prefixes used to form decimal multiples and fractions Prefix Chinese name Prefix English name Symbol Factors represented Prefix Chinese name Prefix English name Symbol Factors represented deci d 10-1 pico pp 10-12 centi centi 10-2 kilo kilo K 103 milli milli ｍ 10-3 mega Ｍ 106 micro micro μ 10-6 giga giga Ｇ 109 nano nano ｎ 10-9 tera T 1012 For the sake of generality, the Greek letter Θ will be used in some of the following formulas to represent prefixes without prefixes and decimal fractions (m, μ, n, p). However, it must be noted that Θ itself is not a prefix, but a symbol agreed upon in this article to avoid listing a large number of identical formulas. Therefore, when you see Θ, you must think of it as m, μ, n, p or no prefix; when you need a formula with a parameter without a prefix unit, please remove Θ; and when you need a formula with a parameter with a prefix unit, please replace Θ with the required prefix. 1.2 decibel In electronics, decibel is a standard unit for expressing transmission gain or transmission loss and relative power ratio, etc., and its code is dB (abbreviation of decibel in English). It formally represents multiples, and in essence it can represent multiples after common logarithmic compression processing (transmission gain and transmission loss expressed in decibels, etc., which are essentially dimensionless), and can also represent the parameter value of the agreed reference value (voltage level, power level, electric field strength expressed in decibels, power flux density, spurious radiation power and adjacent channel power relative to the carrier power level, etc., which are essentially dimensionless). The fundamental reason for its use is that logarithmic operations can compress data length and simplify operations (converting multiplication, division, and exponential operations into addition, subtraction, and multiplication operations respectively), which is particularly suitable for expressing the law of exponential changes. Here we agree to use the symbol lg to represent the logarithm with base 10. The dimensionless unit after logarithmic transformation is often called the level unit (the parameter value equal to its reference value is called zero level. There are two other units of level: Bel and Neper. However, since the document [1] stipulates that "decibel is the unified unit of telecommunication transmission", it is not used here. The following words "level" are prefixed with decibel), and the original unit can be called a linear unit. The comparison between decibel and linear value is shown in the following table: decibel value (dB) voltage, current ratio linear value power ratio linear value decibel value (dB) voltage, current ratio linear value power ratio linear value decibel value (dB) voltage, current ratio linear value power ratio linear value 0.0 1.000 1.000 1 1.122 1.259 11 3.548 12.59 0.1 1.012 1.023 2 1.259 1.585 12 3.981 15.85 0.2 1.023 1.047 3 1.413 1.995 13 4.467 19.95 0.3 1.035 1.072 4 1.585 2.512 14 5.012 25.12 0.4 1.047 1.096 5 1.778 3.162 15 5.623 31.62 0.5 1.059 1.122 6 1.995 3.981 16 6.310 39.81 0.6 1.072 1.148 7 2.239 5.012 17 7.079 50.12 0.7 1.084 1.175 8 5.012 6.310 18 7.943 63.10 0.8 1.096 1.202 9 2.818 7.943 19 8.913 79.43 0.9 1.109 1.230 10 3.162 10.00 20 10.00 100.0 The definition of decibel is divided into the following three cases: 1.2.1 Expression of voltage and parameters that are linearly related to voltage Voltage and parameters that are linearly related to voltage are referred to as voltage-type parameters here, denoted by A, and their units are denoted by x . Taking 1x as the reference value, the unit of the level of A is called decibel x, codenamed dBx, and the calculation formula is A(x) A(dBx)=20lg ———— (1) 1x A(dBx) —————— 20 A(x)=10 （2） A can be voltage (electromotive force, terminal voltage), electric field strength and antenna coefficient, x can be V, mV, μV, V/m, mV/m, μV/m and m-1, etc. The corresponding level units are dBV, dBmV, dBμV, dBV/m, dBmV/m, dBμV/m (often written as dBμ) and dBm-1, etc. The conversion formula between the prefixes of the same voltage-type level units (except antenna coefficients) is dBx = dBmx + 60 = dBμx + 120 (3) dBmx = dBμx + 60 (4) 1.2.2 Expression of power and parameters that are linearly related to power Power and parameters that are linearly related to power are referred to as power-type parameters here, represented by B, and their units are represented by x. Taking 1y as the reference value, the level unit of B is called decibel y, codenamed dBy, and the calculation formula is B(y) B(dBy) = 10lg ———— (5) 1y B(dBy) —————— 10 B(y)=10 （6） B can be power or power density, y can be W, mW, μW, W/m2, mW/cm2, μW/cm2, pW/m2, etc. The corresponding units of electrical level are dBW, dBmW (often written as dBm), dBμW, dBW/m2, dBmW/cm2, dBμW/cm2, dBpW/m2, etc. The conversion formula between the same type of power level unit prefixes is dBy = dBmy + 30 = dBμy + 60 (7) dBmy = dBμy + 30 (8) 1.2.3 Expression of power multiples P1 represents input power, radiated power, and carrier power (the corresponding voltage effective value is U1, and the current effective value is I1), P2 represents output power, received power, and stray radiation/adjacent channel power (the corresponding voltage effective value is U2, and the current effective value is I2), and y is still used to represent the unit of P1 and P2. The decibel expression of transmission gain G or transmission loss L is: P2 (y) U2 (I2) G (or L) (dB) = 10lg ———— = 20lg ———— (9) P1 (y) U1 (I1) Here y can be W, mW, μW, kW, MW, etc. The units of P1 (U1, I1) and P2 (U2, I2) should be consistent, and the units of G and L are dB. The level of spurious radiation relative to carrier power P spurious radiation and the level of adjacent channel power relative to carrier power P adjacent channel power are negative numbers, and the unit is generally recorded as dBC (carrier means "carrier" in English), and the expression is: P2(y) P spurious radiation (or P adjacent channel power) (dBC) = 10lg ———— (10) P1(y) In particular, when U1 represents the available sensitivity of the receiver, and U2 represents the voltage of the unwanted signal on the adjacent channel that makes the output signal-to-noise ratio drop back to 12dB when the receiver inputs a useful signal that is 3dB higher than the available sensitivity, and the voltage of the combined frequency of the third-order intermodulation of the two signals that falls into the working frequency of the useful signal (the voltages of the two frequencies should be equal), the decibel values of the two voltage multiples represent the adjacent channel selectivity P adjacent channel selection and intermodulation immunity P intermodulation immunity of the receiver, and the values are positive numbers, and the unit is generally recorded as dBr (relative means "relative" in English), and the expression is: U2(y) P adjacent channel selection (or P intermodulation immunity) (dBr) = 20lg ———— (11) U1 (y) In addition, antenna gain and noise figure can also be included in this category, see Section 6 for details.
2 RF voltage RF voltage generally refers to the voltage amplitude of the signal at the frequency studied in the radio station, instrument RF level and antenna system. According to the detection method, it can be divided into average value (AV) voltage, root mean square value (RMS) voltage, peak value (PEAK) voltage, etc., hereinafter referred to as voltage. Conventionally, the open circuit voltage at the output end of the signal generator and the receiving antenna is called electromotive force, represented by ein; and when it is connected to a load (such as a communication receiver, a field strength meter, a test receiver, a spectrum analyzer, the receiving end of a comprehensive tester, etc., collectively referred to as a receiving device, and a dummy load), the voltage between its output end and the input end of the connected load is called the terminal voltage, represented by Vin. The linear units of voltage are usually V, mV, and μV, and the corresponding level units are dBV, dBmV, and dBμV, respectively. The conversion between voltage units with different prefixes can be done using equations (3) and (4). To distinguish between electromotive force and terminal voltage, (emf) or (EMF) is usually added after the electromotive force unit, and (cc) is added after the terminal voltage unit or no indication is given. When the impedance of the output terminal of the signal generator or receiving antenna matches the load impedance, the electromotive force is twice the terminal voltage, that is, ein (ΘＶ) = 2 Vin (ΘＶ) (12) ein (dBΘＶ) = Vin (dBΘＶ) + 6.02 (13) The conversion formulas for other parameters to received power are Pr (dBm) = Vin (dBμＶ) - F (dB) (14) In the above equation, F is the conversion coefficient, F (dB) = 90 + 10lgR, and R is the input impedance of the receiving device. When the impedance is 50Ω, F = 106.99dB, and when the impedance is 75Ω, F = 108.75dB. E (dBμV/m) = Vin (dBμV) + K (dBm-1) (15) S (dBW/m2) = Vin (dBV) + K (dBm-1) - 25.76 (16) Where K is the antenna coefficient, see Section 7 for details.
3 RF power RF power generally refers to the arithmetic mean power output to the load at the frequency studied in the radio, instrument RF level and antenna system within a specific RF cycle, hereinafter referred to as power. It is divided into peak envelope power, average power, carrier power, etc. It is usually represented by P. The linear units of power are usually W, mW, μW, and the corresponding level units are dBW, dBmW (often written as dBm), dBμW. The conversion between power units with different prefixes can be used using equations (7) and (8). Transmit power is generally represented by Pt (transmit means "transmit"), and receive power is generally represented by Pr (receive means "receive"). The conversion formula between receive power and other parameters is Vin (dBμV) = Pr (dBm) + F (dB) (17) E (dBμV/m) = Pr (dBm) + F (dB) + K (dBm-1) (18) S (dBW/m2) = Pr (dBm) + F (dB) + K (dBm-1) - 25.76 (19)
4 Electric field strength Electric field strength is the voltage induced by an antenna with a length of 1 meter (m), referred to as field strength, and is usually represented by E. The linear units of field strength are usually V/m, mV/m, μV/m, and the corresponding level units are dBV/m, dBmV/m, dBμV/m (often written as dBμ). The conversion between field strength units with different prefixes can be done using equations (3) and (4). The conversion formula between field strength and other parameters is Vin (dBΘV) = E (dBΘV/m) - K (dBm-1) (20) Pr (dBm) = E (dBμV/m) - F (dB) - K (dBm-1) (21) S (dBW/m2) = E (dBV/m) - 25.76 (22) S (dBμW/cm2) = E (dBμV/m) - 125.76 (23)
5 Power Flux Density Power flux density is the radiation power of radio waves incident on unit area, referred to as power density, usually represented by S. Average power density is the average radiation power of radio waves incident on unit area. The linear units of power density are usually W/m2, mW/cm2, μW/cm2, and pW/m2, and the corresponding level units are dBW/m2, dBmW/cm2, dBμW/cm2, dBpW/m2, etc. For the conversion between power density units, equations (7) and (8) can be used when the area units are the same. The conversion formula for different area units is S (Θ W/m2) = 100 S (Θ W/cm2) (24) S (dBΘ W/m2) = S (dBΘ W/cm2) + 40 (25) The conversion formula for the linear value between power density and field strength is S (W/m2) = E2 (V/m) / 120π (26) S (μW/cm2) = E2 (μV/m) / (120π × 1010) (27) The conversion formula between power flux density and other parameters is E (dBV/m) = S (dBW/m2) + 25.76 (28) E (dBμV/m) = S (dBμW/cm2) + 125.76 (29) Vin (dBV) = S (dBW/m2) - K (dBm-1 )＋２５.７６ （３０） Ｐｒ （ｄＢｍ）＝Ｓ（ｄＢＷ/m2）－Ｆ（ｄＢ）－Ｋ（ｄＢm-1 ）＋２５.７６（３１）
6 Antenna Power Gain 4π times the ratio of the radiation intensity of an antenna in a certain direction (the power radiated by the antenna per unit solid angle) to the net power received by the antenna from its signal source is called the power gain of the antenna in that direction, or antenna gain for short. The maximum value of the antenna gain is called the peak power gain of the antenna[2]. The antenna gain usually refers to the peak power gain of the antenna, while the non-peak power gain is often specified as the gain in a certain direction. There is a more common definition of the antenna gain relative to the standard antenna: the ratio of the radiation intensity of the antenna under study in the direction of maximum radiation to the maximum radiation intensity generated at the same point by a standard antenna with the same input power as the antenna under study[3]. To be precise, the antenna gain under this definition should be called the relative gain of the antenna. When an ideal isotropic radiator (also called a point source radiator or non-directional antenna) is used as the standard antenna, the definition of relative gain is equivalent to the definition of peak power gain mentioned above. The transmit antenna gain is generally represented by Gt, and the receive antenna gain is generally represented by Gr. The linear unit of antenna gain is times. The gain of an isotropic radiator as the standard antenna is called absolute gain or non-directional gain, and its decibel unit is dB or dBi (isotropic means "isotropic" in English). The decibel unit of a half-wave dipole antenna as the standard antenna is dBd (dipole and doublet both mean "symmetrical dipole" and "dipole" in English). The conversion formula between the two is G (relative to the multiple of the isotropic antenna) = 1.64G (relative to the multiple of the half-wave dipole antenna) (32) G (dBi) = G (dBd) + 2.15 (33)
7 Antenna factor The antenna factor is the ratio of the field strength at the antenna point to the voltage at the output end of the antenna (or antenna including the cable) when the load impedance is matched. It is usually represented by K or Ke (K is used in this article) and the unit is m-1 , decibel is expressed as dBm-1 (the unit of the antenna coefficient is m, which is the symbol of the length unit meter), that is, E(ΘＶ/m) K(m-1) = —————— (34) Vin(ΘＶ) K(dBm-1) = E(dBΘＶ/m) - Vin(dBΘＶ) (35) Reference [3] stipulates that the antenna coefficient includes the effective height of the antenna, the loss of the converter, the loss of the cable, and the mismatch loss between the cable and the receiver, while reference [4] states that the antenna coefficient usually does not include the cable loss. This article is based on reference [3]. The conversion formula between the antenna coefficient and the antenna gain is K(dBm-1) = 20lgf(MHZ) - Gr(dB d) + br-31.92 (36) In the formula, br is the cable loss. If the antenna gain Gr already includes the cable loss, this item should be removed. In addition, if it is necessary to lengthen the cable of an antenna with a known antenna coefficient, then the actual K value should add the loss of the lengthened cable.
8 Noise Factor The noise factor is the ratio of the input signal-to-noise power ratio to the output signal-to-noise power ratio of a receiver or active device. The linear value is represented by Fn and is dimensionless; the decibel value is represented by NF. Some literature calls the noise factor expressed in decibels the noise index. Fn = 1 + Te/T0 where Te is the input equivalent noise temperature and T0 is the specified room temperature of 290K. NF (dB) = 10lgFn
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