Communication Systems Prof. Kuo, Chungming

Chapter 1 Decibel Computations (cont.)

Decibel Computations Widely employed in the communications industry. Decibel forms are vital to understanding the many system specifications and performance standards. Arguably not as essential today, but the practice of utilizing decibel forms is so widespread that the tradition will likely continue.

Decibel Computations (cont.) This module covers basic decibel definitions and how they are applied in systems analysis.

Important Logarithmic Identities

Block Diagram for Defining Gain

Power Gain Definitions Absolute Power Gain: Decibel Power Gain:

Power Loss Definitions Absolute Power Loss: Decibel Power Loss: Note:

Useful Decibel Patterns

Conversion from Decibel Gain to Absolute Gain Start with: Divide both sides by 10

Conversion from Decibel Gain to Absolute Gain (cont.) Raise both sides to power of 10 By a similar approach

Decibel Voltage and Current Forms Assume a resistance R at both input and output

Decibel Voltage and Current Forms (cont.) Assume a resistance R at both input and output

Some Common Decibel Values

Example 1: An amplifier has an absolute power gain of 175. Determine the decibel gain. Some Common Decibel Values (cont.)

Example 2: An amplifier gain is given as 28 dB. Determine the absolute power gain. Some Common Decibel Values (cont.)

Example 3: Assuming equal input and output resistances, determine the voltage gain in Some Common Decibel Values (cont.)

Example 4: In a lossy line, only 28% of the input power reaches the load. Determine the decibel gain and loss. Some Common Decibel Values (cont.)

Decibel Reference Levels In its basic form, the decibel involves a logarithmic ratio and is dimensionless. However, there are various portions of the industry that have adopted decibel measures relative to some standard reference level. All of these forms have some modifier attached to the unit; e.g., dBm, dBf, etc.

Typical Decibel Reference Levels

Conversion Between Decibel Signal Levels

Example 5 A signal has a power level of 100 mW. Express the level in dBm, dBW, and dBf.

Decibel Gain Combined with Decibel Signal Levels Divide both sides by the same reference level, take logs of both sides, multiply by 10, and expand. The quantity x below represents any reference standard; e.g., m.

Cascade System It is assumed that impedance (resistance) levels are matched at all junctions.

Cascade Decibel Gain Analysis Take logs of both sides, expand, and multiply by 10. Apply dB forms to all terms.

Example 6 For system below, determine (a) system absolute gain, (b) system decibel gain from (a), and (c) system decibel gain from individual stages.

Example 6 (cont.)

Example 7 The source below is connected to the system of Example 6. Find (a) power levels in watts at all junctions and (b) corresponding dBm levels.

Example 7 (cont.)

Example 8 For the system below, determine power and voltage levels at each point and the required gain of the output receiving amplifier based on 75-  matching at all junctions.

Data for Example 8

Example 8: Computations

Example 8: Computations (cont.) Alternately,

Decibel Signal-to-Noise Ratios P = average signal power in watts N = average noise power in watts

Example 9 At a given point, signal power is 5 mW and noise power is 100 nW. Determine absolute and dB S/N ratios.

Example 9 (cont.) Alternately, At a given point, signal power is 5 mW and noise power is 100 nW. Determine absolute and dB S/N ratios.

Summary A decibel is not an absolute unit, but is based on a logarithmic power ratio. Decibel measures are widely employed throughout the electronics industry, but especially in the communications area.

Summary (cont.) Decibel level units are based on a standard reference and dB is always accompanied by a modifier in that case, namely, dBm. The decibel gain of a complete system is the sum of the individual dB gains. A decibel level output is the sum of the decibel level input and the decibel gain.