ELEC 425 Interference Control in Electronics Lecture 1(c) Review of Decibels & Decibel Arithmetic

Transcription

1 Dr. Gregory J. Mazzaro Fall 2017 ELEC 425 Interference Control in Electronics Lecture 1(c) Review of Decibels & Decibel rithmetic THE CITDEL, THE MILITRY COLLEGE OF SOUTH CROLIN 171 Moultrie Street, Charleston, SC 29409

2 2 Logarithms x N b log N x where N = positive number ( linear value ) b b = the base of the logarithm x = the exponent of the logarithm -- a way to easily write/compare numbers that are very large and/or very small, simultaneously -- an alternative to scientific notation using b = 10 ( base-10 ) N x , ,000,000 6 Typical electric fields range from 1 m/m to 200 /m 8 orders of magnitude. The decibel scale compresses this data to a narrower range of numbers.

3 Gain & Decibels Gain () refers to the ratio of put-to-input voltage, current, field, power, etc. p v in p v 20log10 p 10log10 in in in in in p W W in p Decibels are a convenient format used to express very high/low gain (up/down to very high/low values of voltage, field, power). in p,1 p,2 p p,1 p,2 p p,1 p,2 3

4 Gain (/) Gain () 4 Decibels: The decibel scale is a logarithmic log N x scale that uses base b = By convention, gain in decibels is v v log 10 v v 10log 10 p p v 3 v

5 ower (m) ower (mw) 5 Decibels: m The decibel scale is a logarithmic log N x scale that uses base b = By convention, power in decibels (referenced to 1 milliwatt) is m 1 2 mw 3m 10log 10 1 mw W m

6 Field (m/m) Field (m/m) 6 Decibels: m/m The decibel scale is a logarithmic log N x scale that uses base b = By convention, electric field in decibels (referenced to 1 microvolt per meter) is E μ/m E 1 2μ/m 6 μ/m E 20log 10 1μ m E μ/m 3 E μ/m

7 Decibels: Circuits & Gain I in I in R 2 in in R 2 L v i p I I in in in v 20log10 in I i 20log10 Iin p 10log10 in where in,, I in, I are assumed to be RMS values. 7

8 Decibels: oltage, Current, ower, Field I in I I I 20log 1 m m 10 20log 1μ μ 10 I 20log 1 m m 10 I 20log 1μ μ 10 E E E 20log 1 m/m m/m 10 E 20log 1μ/m μ/m 10 10log 1 mw mw 10 8 where, I, E are assumed to be RMS values.

9 Examples: Decibel Conversions Express the ratios of the following quantities in decibels: (a) a power of 20 W to a power of 1 mw (b) a current of 2 m RMS to a current of 0.5 RMS Convert the following quantities to the specified decibel units: (c) 20 m/m to m/m (d) 300 mw to m 9

10 Dr. Gregory J. Mazzaro Fall 2017 ELEC 425 Interference Control in Electronics Lecture 1(d) Cable Losses & High-Frequency Signal Sources THE CITDEL, THE MILITRY COLLEGE OF SOUTH CROLIN 171 Moultrie Street, Charleston, SC 29409

11 Transmission-Line Theory complete mathematical model for the transmission-line circuit yields (in Section 1.5.1) 2 d 2 dz 0 2 j r jl g jc The general solution to this wave equation is z e e, I z I e I e z z z z which is a pair of waves: one travels from source to measurer ; the other travels from measurer to source. e z 0 The ratio of voltage-to-current for one of the waves is the characteristic impedance, Z C e z 0 Z C r jl I g jc

12 Circuit Models for Instruments t a particular frequency (or within a narrow band of frequencies) 13

13 Matched System (50 W) system is matched when the Thevenin impedance of the source, the characteristic impedance, and the Thevenin impedance of the measurer are equal. Our industry standard is 50 W. When all impedances are matched, the solution is z e, I z I e For a mismatched load/cable, the signal z z 0 0 which is one wave, traveling from source to measurer. source put may be determined using e z 0 14

14 Cable (ower) Loss The system is assumed to be matched (usually to 50 W). z = 0 z = L When all impedances are matched, the solution is z e, I z I e, j z z 0 0 which carries the time-average power z avg z Re z I z e coszc 2 2 Z C attenuation with distance into the cable z Cable loss (in ) is calculated from L e L 2 10log L where is the attenuation constant in Nepers per meter (Np/m). 15

15 Example: Cable Loss 50-W source is attached to a 50-W signal measurer with 300 ft of RG58U coaxial cable. The source is tuned to a frequency of 100 MHz, and the dial indicates an put of 15 m. t this frequency, the cable loss is 4.5 / 100 ft. Determine the (RMS) voltage at the input to the signal measurer in m log 1 mw mw 10 v 20log 1μ μ 10

16 Example: Signal Source Output 50-W source is attached to a measurer whose input impedance is 25 W. The dial on the signal generator indicates that it is putting a level of 20 m. Determine the (RMS) voltage at the input to the signal measurer in m. 18