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MODULE 1-INTRODUCTION TO LOGARITHM AND DECIBEL.pptx
- 1. INTRODUCTION TO LOGARITHMAND DECIBEL
- 2. THE DECIBEL • Thedecibel, db is a logarithmic scale used for comparing two physical quantities especially in electronics. • It is the logarithmic measurement of the ratio of one power to another or one voltage to another. • Is a logarithmic expression used in filter applications as a unit of gain or loss. • It is a unit of logarithmic gain measurement and is commonly used to express amplifier response.
- 3. LOGARITHM • Logarithm, theexponent or power to which a base must be raised to yield a given number. expressed mathematically, x is the logarithm of n to the base b bx = n EXPONENTIAL FORM 𝑙𝑜𝑔𝑏 n=x LOGARITHM FORM • EXAMPLE: 53 = 125 𝑙𝑜𝑔5125 = 3 LOG TO THE BASE 5 OF 125 IS 3
- 4.
- 5. Decibel Applications • thedecibel, db is widely used in many applications. it is used within a wide variety of measurements in the engineering and scientific areas, particularly within electronics, acoustics and also within control theory. • typically the decibel, db is used for defining amplifier gains, component losses (e.g. attenuators, feeders, mixers, etc), as well as a host of other measurements such as noise figure, signal to noise ratio, and many others.
- 7. DECIBEL FORMULA FORPOWER COMPARISONS • The most basic form for decibel calculations is a comparison of power levels. as might be expected it is ten times the logarithm of the output divided by the input. the factor ten is used because decibels rather than bels are used.
- 8. DECIBEL FORMULAS FORVOLTAGE & CURRENT • although the decibel is used primarily as comparison of power levels, decibel current equations or decibel voltage equations may also be used provided that the impedance levels are the same. in this way the voltage or current ratio can be related to the power level ratio. • when using voltage measurements, it is easy to make the transformation of the decibel formula because power = voltage squared upon the resistance:
- 11. • if thevoltage gain(𝐴𝑉) is greater than 1, the dB gain is positive. if it is less than 1, the dB gain is negative which is usually called attenuation. • in this way a positive number of decibels implies a gain, and where there is a negative sign, it implies a loss. • if the value of p2 is greater than p1, then the result is given as a gain, and expressed as a positive value, e.g. +10db. where there is a loss, the decibel equation will return a negative value, e.g. -15db.
- 12. EXAMPLE Given: P2(output power)=100W P1(input power)=100mW=100𝑥10−3= 0.1𝑊 𝐴𝑝 𝑑𝐵 =? Solution: 𝐴𝑃 𝑑𝐵 = 10𝑙𝑜𝑔10 𝑃2 𝑃1 𝐴𝑃 𝑑𝐵 = 10𝑙𝑜𝑔10 100 0.1 𝑨𝑷 𝒅𝑩 =30dB An audio amplifier delivers 100 watts into an 8-ohm speaker load when fed by a 100mw input signal. calculate the power gain of the amplifier in decibels.
- 13. EXAMPLE A PASSIVE RESISTIVE NETWORKIS USED TO PROVIDE AN ATTENUATION (LOSS) OF 10DB, WITH AN INPUT VOLTAGE IS 12V. WHAT WILL BE THE NETWORKS OUTPUT VOLTAGE VALUE. given: 𝐴𝑉 𝑑𝐵 = −10𝑑𝐵 𝑙𝑜𝑠𝑠 v1(input voltage)=12v v2(output voltage)=? solution: 𝐴𝑉 𝑑𝐵 = 20𝑙𝑜𝑔10 𝑉2 𝑉1 -10db= 20𝑙𝑜𝑔10 𝑉2 12 -0.5= 𝑙𝑜𝑔10 𝑉2 12 0.3162= 𝑉2 12 𝑽𝟐=3.79v
- 14. • A POWERAMPLIFIER HAS AN OUTPUT OF 10 W AND A GAIN OF 36 DB. WHAT IS THE POWER INTO THE AMPLIFIER, INPUT POWER?
- 15. NEPER • THE NEPERIS A LOGARITHMIC SCALE BASED ON NATURAL LOGARITHMS TO BASE E. • ALTHOUGH DECIBELS ARE THE MAIN UNIT FOR EXPRESSING THE RATIOS OF GAIN AND LOSS LIKE ELECTRICAL POWER IN ELECTRONIC AND OTHER SYSTEMS, THE NEPER IS ALSO USED. • THE NEPER IS NOT PARTICULARLY WIDELY USED BUT HAS ADVANTAGES IN SOME INSTANCES MATHEMATICAL ADVANTAGES CAN BE USED. • THE NEPER USES THE SYMBOL NP AND IS A LOGARITHMIC UNIT FOR RATIOS OF MEASUREMENTS FIELD AND POWER QUANTITIES, SUCH AS GAIN AND LOSS OF ELECTRONIC SIGNALS.