# What is the meaning of transmission units? What is the units of transmission of signals?

# Transmission Units

The study of transmission units has a unique importance for communication engineer who has to maintain and install telecommunication equipments achieving the standards set up by international consultation committees.

In order to control the quality of wanted signal in the presence of many undesired signals, we should be able to specify the amount of wanted and unwanted signals at a point in the telecommunications network.

The components used in the telecommunication circuit either give loss or gain to the signals they handle. There are certain specific operating conditions to be satisfied for various components without which the optimum performance cannot be obtained from these components. For this, it is essential to define conditions that control those operating conditions. This can be done only if the conditions are specified in terms of certain units of the quantity the components are to handle.

** ****Transmission Impairments**

With analog transmission systems using copper cable there are three major categories of impairments. They are attenuation, noise, and distortion.

**Attenuation:**There are two commonly used processes to compensate (overcome) for attenuation or loss:

(a) Repeaters are the most commonly used devices to compensate for “Loss.” However, repeaters amplify the noise along with the signal resulting in a poor signal to noise ratio.

(b) Signal to Noise Ratio: The ratio of the average signal power (strength) to the average noise power (strength) at any point in a transmission path.

**Noise:**Any random disturbance or unwanted signal on a transmission facility that obscures the original signal. Noise is generally caused by the environment in which the system is operating.**Distortion:**Inaccurate reproduction of a signal caused by changes in the signal’s waveform, either amplitude or frequency, to compensate for distortion equalizers may be used. One type of equalizer used in the analog environment is the load coil. Load coils are used to flatten the frequency response.

**Note:** Generally the higher the frequency the greater the distortion. That is, the higher voice frequencies attenuate at a higher rate than the lower voice frequencies.

Noise and distortion on a carrier facility can be separated into two types:

(a) Predictable impairments that are almost always present on our facilities.

(b) Unpredictable impairments those are transient in nature and difficult to overcome.

#### The Decibel And Neper

** **Historically speaking ‘attenuation’ was first of all defined in terms of the attenuation produced by a standard reference cable known as “mile of standard cable”. It consists of 88 ohms series impedance and 0.54 µF as shunt impedance.

The fundamental objection to this unit was the fact that the attenuation of the standard cable varied with frequency. With the introduction of systems operating over different frequency ranges, it became necessary to define a unit which was independent of frequency .The unit which represents the useful and convenient concepts in connection with the transmission of signals over telephone lines has been named and defined as “Bel”(which comes from the name Alexander Graham Bell -the inventor of Telephone). In practice ,however , a smaller and more convenient unit called decibel (abbreviated as dB) is used.

##### Decibel (dB)

One tenth of the common logarithm of the ratio of relative powers, equal to 0.1 B (bel). The decibel is the conventional relative power ratio, rather than the bel, for expressing relative powers because the decibel is smaller and therefore more convenient than the bel. The ratio in dB is given by

X = log P_{2}/P_{1} B i.e. = 10 log P_{2}/P_{1} dB

where P _{1} and *P* _{2} are the actual powers. Power ratios may be expressed in terms of voltage and impedance, *E* and *Z*, or current and impedance, *I* and *Z*. Thus dB is also given by;

X = 20 log V_{2}/ V_{1} dB. (when Z _{1} = *Z* _{2} )

Note: The dB is used rather than arithmetic ratios or percentages because when circuits are connected in tandem, expressions of power level, in dB, may be arithmetically added and subtracted. For example, in an optical link if a known amount of optical power, in dBm, is launched into a fiber, and the losses, in dB, of each component (e.g., connectors, splices, and lengths of fiber) are known, the overall link loss may be quickly calculated with simple addition and subtraction.

##### Example 1

Let us look at the following network:

**1W——Network—–2W**

The input is 1W and its output 2W, therefore,

Gain = 10 log (output)/(input) dB.

= 10 log 2/1 dB= 10 (0.3010) dB=3.101 dB

= 3dB approximately

##### Example 2

Let us look at another network:

**1000W——Network—–1W**

Loss = 10 log Input/Output =10 log 1000/1 dB =10 log 10^{3 }dB

=30 log 10 dB

= 30 dB

Thus a network with an input of 5 W and output of 10 W is said to have

Gain = 10 log 10/5 dB

= 10 log 2 dB

=3.103 dB

= 3 dB.

Let us remember that doubling the power means a 3 dB gain; likewise halving the power means a 3dB loss.

##### Example 3

Consider a network with a 13 dB gain:

**0.1W——Network 13 db gain—–?**

Gain = 10 log P2/P1 dB = 10 log P2/0.1 dB =13db

i.e., log P2/0.1 = 1.3 or P2/0.1 = antilog 1.3 or

P2 = 0.1 antilog 1.3

P2 = 2W

##### Example 4

Consider the following network

**1W——Network 27 db Loss—–?W**

What is the power output of this network? To do this without pencil and paper, we would proceed as follows:

Suppose the network attenuated the signal by 30 dB. Then the output would be 1/1000 of the input or 1mW.

Now 27 dB loss is 3dB less than 30 dB.

Thus the output would be twice 1m W i.e., 2mW.

(Because the loss is less by 3 dB, the corresponding output will be more i.e. double but not half)

It is quite simple. Thus, if we have multiples of 10 or 3 up or 3 down from these multiples, we can work it out in our mind without pencil and paper.

##### Example 5

Let us take the next example.

**10W——Network 6 db Loss—–3W**

We know that the 3 dB gain represents approximately 2 times power gain. So 6 dB gain means 4 times the gain.

Therefore, the output = 10×4 = 40 (Likewise a 6 dB loss would represent approx. 1/4 of the input power as output i.e. 10/4 = 2.5W)

##### Example 6

Consider a network of 33 dB gain with an input level of 0.15W. What would be the output?

30 dB represents multiplying the input power by 1000 and 3 additional dBs double it. In this case the input power is multiplied by 2000.

Thus the answer is 0.15 x2000 = 300 W.

Now work out the output in the same case if

- the gain was 36 dB
- the loss was 33 dB

The transmission unit normally used is the decibel. The other unit, however, is also used in some East European countries.

##### NEPER

The natural logarithm of the ratio of two voltages (or currents) expresses the loss or gain in Nepers, N

i.e. X= log_{e} V1/V2 (N)

when the loss (gain) is X Neper, V1 and V2 are voltages, then

e^{x} = V1/V2

Example

The loss of a transmission system is 1N when 2.72 V input voltage produces 1 V output voltage.

Comparing powers, X= 1/2 log_{e }P1/P2 (N) or e^{2x} = P1/P2

Other transmission units 1 deciNeper (dN) = 0.1 N

1 Centi Neper (cN) = 0.01N

1 MilliNeper (mN) = 0.001 N

** **

#### Basic derived decibel units

** ****DBm**

Till now decibel has referred to ratios or relative units. We cannot say that the output of an amplifier is 33 dB. We can say that an amplifier has a gain of 33 dB or that a certain attenuator has a 6 dB loss. These figures or units don’t give any idea whatsoever of absolute level. Whereas, several derived decibels units do.

Perhaps the dBm is the most common of these. By definition dBm is a power level related to 1 mw. The most important relationship to remember is:

0 dBm = 1mW.

The dBm formula may then be written as:

Power (in dBm) = 10 log Power (mW)/(1mW)

**Example**

An amplifier has an output of 20 W; what is its output in dBm?

Power (dBm) = 10 log 20 W/1 mW = 10 log 20×10^{3 }mW/1mW = +43 dBm.

(The plus sign indicates that the quantity is above the level of reference, 0 dBm.)

**dBmO**

Decibel referred to 1 mw at zero (0) Transmission level point. dBmO is a measure of power with reference to Zero dBm at the Reference Transmission Level Point (RTLP).

The RTLP is also known as Zero Transmission Level Point (0TLP). Powers measured at any transmission level point can be expressed in dBmO, by correcting the power measured for the difference in level between the point of measurement and the RTLP.

For example, a level of +25 dBm measured at a +17 dB transmission level point is equivalent to 8 dBmO. Conversely a level of +8 dBmO is also equivalent to +3 dBm measured at a -5 dB transmission level point. A level expressed in dBmO is, therefore, only a relative level.

##### Conversion from Neper to decibel and Vice Versa

** **We know that decibel is fundamentally a unit of power ratio but it can be used to express current ratios when the resistive components of the impedance, through which the current flows, are equal.

The Neper, on the other hand, is fundamentally a unit of current ratio but it can also be used to express power ratios when the resistive components, of the impedance, through which the current flows, are equal.

Because of its derivation from the exponential **e**, the Neper is the most convenient unit for expressing attenuation in theoretical works. The decibel, on the other hand, being defined in terms of logarithms to base **10**, is a more convenient unit in practical calculations using the decimal system.

The conditions under which the two units may be used can be summarised in the following equations, the notation of which is indicated in Fig below.

Where Z1 and Z2 are characteristic impedances

R1 and R2 are pure resistances

G1 and G2 are leakances

b1 and b 2 are phase angles

X1 and X2 are reactance.

Attenuation in dB= 8.686 x attenuation in Nepers

(provided that R1 = R2)

Attenuation in Nepers= 0.1151 x attenuation in dB

(provided that R1 =R2)

**Other Units**

In Analogue Transmission system, the quality of communication is mainly assessed by the value of Signal to noise ratio.

#### Signal-to-Noise Ratio

It is popularly known as SNR. SNR is the ratio of signal power to the noise power at any point in a circuit. This ratio is usually expressed in Decibels (dB). For satisfactory operation of a channel the value of SNR should be sufficiently high i.e., the signal power should be sufficiently higher than the noise power.

SNR at any point in a circuit is given as SNR = S/N = Signal Power / Noise Power

Both powers are expressed in watts.

Expressing dBs: SNR = 10 log_{10 }(S/N) dB.

Example: Signal voltage Vs = 0.923 µV; Noise voltage Vn = 0.267 µV, then calculate the

signal-to-noise ratio.

S/N = Vs^{2} / Vn^{2} = 0.923/0.267)^{2} = 11.95

In decibels, S/N = 10 log10 (11.95) = 10.77 dB.

** **In Digital Transmission system, the quality of communication is mainly assessed by two factors.

- BER (Bit Error Ratio)
- Jitter

These two factors can be taken as Quality Factors as they are used for judging the quality of Digital Transmission.

**Bit Errors**

In the digital transmission, the bits transmitted at the transmitting end (1 or 0 ) are not always detected as 1 or 0 at the receiving end. When the transmitted bit 1 or 0 is not identified as 1 or 0 at the receiver, the bit is counted as an **error bit**.

For assessing the real error performance, the **bit error ratio** (BER) is to be calculated instead of actual error bits.

**Bit Error Rate (BER)**

** **The BER is the measure or error bits with respect to the total number of bits transmitted in a given time. The total number of bits transmitted can be known from the bit rate of the digital signal. The bit rate is the number of bits transmitted in one second and is specified for each transmission system. Hence, the total number of bits transmitted in a given time can be counted. In the measurement of BER, generally the measuring instrument measures the number of bits transmitted in a given time.

The time setting can be from a few seconds to a few hours, depending on the feasibility. The standards are set by ITU (International Telecommunication Union). The time set for the measurement of BER, is called **gating time**. Larger the gating time better is the assessment of BER. But for the measurement of BER, the Digital Equipment has to be taken off-line.

Digital communication can just run with one error bit in one thousand bits received. For more than one error bit, in one thousand bits received, communication gets affected.

For good quality communication, the requirement is, not more than one error bit in one million bits.

**JITTER**

Abrupt and unwanted variations of one or more signal characteristics, such as the interval between successive pulses, the amplitude of successive cycles, or the frequency or phase of successive cycles. Jitter must be specified in qualitative terms (*e.g.,* amplitude, phase, pulse width or pulse position) and in quantitative terms (*e.g.,* average, RMS, or peak-to-peak). The low-frequency cut-off for jitter is usually specified at 1 Hz. *Contrast with* drift, wander.

** **Short term variations of the significant instances of a digital signal from their reference position in time.( Short term frequency equal to or greater than 10 Hz.). Long term variations of significant instances of a digital signal from their ideal positions in time, are called wander. (Long-term variations – frequency less than 10 Hz).

**Drift:** A comparatively long-term change in an attribute or value of a system or equipment operational parameter. The drift should be characterized, such as “diurnal frequency drift” and “output level drift.” Drift is usually undesirable and unidirectional, but may be bi-directional, cyclic, or of such long-term duration and low excursion rate as to be negligible.

**Wander:** Relative to Jitter and swim, long-term random variations of the significant instants of a digital signal from their ideal positions. Wander variations are those that occur over a period greater than 1 s (second). Jitter, swim, wander, and drift have increasing periods of variation in that order.

** ****Swim:** Slow, graceful, undesired movements of display elements, groups, or images about their mean position on a display surface, such as that of a monitor. Swim can be followed by the human eye, whereas Jitter usually appears as a blur.

*Jitter, like BER, is another transmission impairment. It is not very significant in the case of voice signal transmission but it has a great impact in the transmission of data signals, especially with high-speed digital transmission. The present bit rates are as high as 565 Mb/s and (140 x 16) Mb/s. Today Jitter is considered as a performance parameter of any digital transmission system.*

For example, Jitter due to unwanted phase change is called Phase Jitter. The amount of change of phase, converted into time, is generally expressed in milli-seconds or nano-seconds.

BER and Jitter are the unwanted by products of any transmission system and they get associated with the transmission path and affect the quality of transmission. Bit Errors beyond a limit, affect the communication and Jitter in the digital transmission system, is a source of generation of errors.

Digital Transmission Analyser (DTA) is used for the measurement of both BER and Jitter.

**Digital Transmission – Performance Criteria ( General) **

1 in 10^{6 }(1.OE – 6): Better

1 in 10^{5 }(1.OE – 5): Good

1 in 10^{4 }(1.OE – 4) : Reasonably good

1 in 10^{3 }(1.OE – 3) : Just Acceptable

More than 1 in 10^{3 }: Unacceptable

Bit errors greatly affect data service.

For data channels 1 in 10^{9 }(1.OE – 9) is normally realizable.

**Quality Parameters**

** **To pin point the exact number of seconds or minutes, in which the bit errors take place and up to what extent, the quality parameters are defined.

The quality parameters are:

- Error Seconds (ES)
- Severely Error Seconds (SES)
- Non Severely Error Seconds (NSES)
- Degraded Minutes (DM).

**Error Seconds (ES):** Number of one-second intervals with one or more errors.

**Severely Error Seconds (SES):** Number of one-second intervals with an error rate, worse than 1.OE-3

**Non-Severely Error Seconds (NSES): **Number of one-second intervals with an error rate, better than or equal to 1.OE-3.

**Degraded Minutes (DM): **Number of one-second intervals with a bit error rates worse than 1.OE-6.

**Available and non-available time**

A period of available time begins with a period of ten consecutive seconds each of which has a BER better than 1.0E-3. These 10 seconds are considered to be available time.

A period of unavailable time begins when the bit error rate in each second is worse than 1.0E-3 for a period of 10 consecutive seconds. These 10 consecutive seconds are considered to be unavailable times.

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