Biblio5

624 LEARNING DECIBELS AND THEIR APPLICATIONS

Figure C.2 Flat response (idealized) versus C-message weighting. The hatched area shows how we arrive at approximately a 2-dB noise advantage for C-message weighting. We can only take advantage of C-message improvement for speech telephony. For data transmission we must use flat response.

Value in (−) dBm c 10 log(pW × 10−9).

Value in pWp c value in pW × 0.56.

−90 dBm c −2 dBrnC and thus − 92 dBm c 0 dBrnc(white noise loading)

−92.5 dBmp c −90 dBm(flat, white noise) 1 pWp c −90 dBmp

value in dBm c 10 log(value in pWp × 10−9) + 2.5 dB dBrnC c 10(log pWp × 10−9) − 0.5 dB + 90 dB

value in pW × 0.56 c value in pWp value in pWp/ 0.56 c value in pW

Table C.1 summarizes some of the relationships we have covered for flat and weighted noise units.

Example 1. A hypothetical reference circuit shall accumulate no more than 10,000 pWp of noise. What are the equivalent values in dBrnC, dBm, and dBmp?

dBrnC c 10(log 10, 000 × 10−9) − 0.5 dB + 90 dB c 39.5 dBrnC.

(−) dBm c 10 log(10, 000 × 10−9) + 2.5 dB

c−47.5 dBm.

Source: Based on Table 4.2, p. 60, Ref. 1.

dBmp c 10 log 10, 000 pWp × 10−9

c−50 dBmp.

Example 2. We measure noise in the voice channel at 37 dBrnc. What is the equivalent noise in pWp?

37dBrnC c 10(log X × 10−9) − 0.5 + 90 dB.

−52.5 c 10(log X × 10−9).

−5.25 c log X × 10−9.

antilog(−5.25) c 5623 × 10−9.

Answers: 1: 5 pWp. 2: −43.28 dBmp. 3: −49.5 dBmp. 4: 2238 pWp c −56.5 dBmp

c−54 dBm. 5: 42.5 dBrnC. 6: −43 dBmp c −40.5 dBm. 7: 1120 pWp. 8: 35.5

dBrnC.

C.8 INSERTION LOSS AND INSERTION GAIN

When dealing with the broad field of telecommunication engineering, we will often encounter the terms insertion loss and insertion gain. These terms give us important information about a two-port network in place in a circuit. Two-port just means we have an input (port) and an output (port). A major characteristic of this device is that it will present a loss in the circuit or it will present a gain. Losses and gains are expressed in dB. In the following we show a simple circuit terminated in its characteristic impedance, Z0.

626 LEARNING DECIBELS AND THEIR APPLICATIONS

Ω

We now insert into this same circuit a two-port network as follows:

First for the case of insertion loss: Let us suppose the device is an attenuator, a length of waveguide, a mixer with loss, or any other lossy device. Suppose we are delivering power p2 to the load ZL with the network in place and power p0 with the network removed. The ratio expressed in dB of p0 to p2 is called the insertion loss of the network:

Insertion lossdB c 10 log(p0/ p2).

If ZL equals Z0, we can easily express insertion loss as a voltage ratio: Insertion lossdB c 20 log(E0/ E2).

If the network were one that furnished gain, such as an amplifier, we would invert the ratio and write:

Insertion gaindB c 10 log(p2/ p0)

or, for the case of voltage,

Insertion gaindB c 20 log(E2/ E0).

This may seem to the reader somewhat redundant to our introductory explanation of dBs. The purpose of this section is to instill the concepts of insertion loss and insertion gain. If we say that that waveguide section had an insertion loss of 3.4 dB, we know that the power would drop 3.4 dB from the input to the output of that waveguide section. If we said that the LNA (low noise amplifier) had an insertion gain of 30 dB, we would expect the output to have a power 30 dB greater than the input.

C.9 RETURN LOSS

Return loss is an important concept that sometimes confuses the student, particularly when dealing with the telephone network. We must remember that we achieve a maximum power transfer in an electronic circuit when the output impedance of a device (network) is exactly equal to the impedance of the device or transmission line connected to the output port. Return loss tells us how well these impedances match; how close they are to being equal in value (ohms) to each other.

Consider the following network’s output port and its termination. The characteristic impedance (Z0) of the output of the network is 600 Q .

We have terminated this network in its characteristic impedance (Z0). Let us assume for this example that it is 600 Q . How well does the network’s output port match its characteristic impedance? Return loss tells us this. Using the notation in the preceding example, return loss is expressed by the following formula:

Return lossdB c 20 log(Zn + Z0)/ (Zn − Z0).

First let us suppose that Zn is exactly 600 Q . If we substitute that in the equation, what do we get? We have then in the denominator 0. Anything divided by zero is infinity. Here we have the ideal case, an infinite return loss; a perfect match.

Suppose Zn were 700 Q . What would the return loss be? We would then have:

Return lossdB c 20 log(700 + 600)/ (700 − 600)

c20 log(1300/ 100) c 20 log 13

c22.28 dB.

Good return loss values are in the range of 25 dB to 35 dB. In the case of the telephone network hybrid, the average return loss is in the order of 11 dB.

This diagram is the special situation of the 2-wire/ 4-wire conversion using the hybrid transformer, a 4-port device. Let us assume that the subscriber loop/ local exchange characteristic impedance is 600 Q . We usually can manage to maintain good impedance match with the 4-wire trunks, likewise for the balancing network, often called a compromise network. However, the 2-wire side of the hybrid can be switched into very short, short, medium, and long loops, where the impedance can vary greatly.

We will set up the equation for return loss assuming that at this moment in time it is through connected to a short loop with an impedance of 450 Q ; the impedance of the balancing network is 600 Q , which is Z0. We now calculate the return loss in this situation:

Return loss dB c 20 log(600 + 450)/ (600 − 450)

c20 log(1050/ 150) c 20 log 2.333

c7.36 dB.

ed.) of Transmission Systems for Telecommunications (Bell Telephone Laboratories, New York, 1959, Vol. I, pp. 2–3):

In order to specify the amplitudes of signals or interference, it is convenient to define them at some reference point in the system. The amplitudes at any other physical location can be related to this reference point if we know the loss or gain (in dB) between them. In the local plant, for example, it is customary to make measurements at the jacks of the outgoing trunk test panel, or (if one does not wish to include office effects) at the main frame. For a particular set of measurements, one of these points might be taken as a reference point, and signal or noise magnitudes at some other point in the plant predicted from a knowledge of the gains or losses involved.

In toll telephone practice, it is customary to define the toll transmitting switchboard as the reference point or “zero transmission level” point. To put this in the form of a definition:

The transmission level at any point in a transmission system is the ratio of the power of a test signal at that point to the test signal power applied at some point in the system chosen as a reference point. This ratio is expressed in decibels. In toll systems, the transmitting toll switchboard is usually taken as the zero level or reference point.

Frequently the specification of transmission level is confused with some absolute measure of power at some point in the system. Let us make this perfectly clear. When we speak of −9-dB transmission level point (often abbreviated “the −9 level”), we simply mean that the signal power at such a point is 9 dB below whatever signal power exists at the zero level point. The transmission level does not specify the absolute power in dBm or in any other such power units. It is relative only. It should also be noted that, although the reference power at the transmitting toll switchboard will be at an audio frequency, the corresponding signal power at any given point in a broadband carrier system may be at some carrier frequency. We can, nevertheless, measure or compute this signal power and specify its transmission level in accordance with the definition we have quoted. The transmission level at some particular point in a carrier system will often be a function of the carrier frequency associated with a particular channel.

Using this concept, the magnitude of a signal, a test tone, or an interference (level) can be specified as having a given power at a designated level point. For example, in the past many long toll systems had 9-dB loss from the transmitting to the receiving switchboard. In other words, the receiving switchboard was then commonly at the −9-dB transmission level. Since noise measurements on toll telephone systems were usually made at the receiving switchboard, noise objectives were frequently given in terms of allowable noise at the −9-dB transmission level. Modern practice calls for keeping loss from the transmitting terminals to the receiving terminals as low as possible, as part of a general effort to improve message channel quality. As a result, the level at the receiving switchboard, which will vary from circuit to circuit, may run as high as −4 dB or −6 dB. Because of this, requirements are most conveniently given in terms of the interference that would be measured at zero level. If we know the transmission level at the receiving switchboard, it is easy to translate this requirement into usable terms. If we say, some tone is found to be −20 dBm at the zero level and we want to know what it would be at the receiving switchboard at −6 level, the answer is simply −20 − 6 c −26 dBm.

Quoting from the 4th edition of Transmission Systems for Communications (Ref. 2):

630 LEARNING DECIBELS AND THEIR APPLICATIONS

Expressing signal mangitude in dBm and system level in dB provides a simple method of determining signal magnitude at any point in a system. In particular, the signal magnitude at 0 TLP is S0 dBm, then the magnitude at a point whose level is Lx dB is

Sx c S0 + Lx

The abbreviation dBm0 is commonly used to indicate the signal magnitude in dBm at 0 TLP. Of course, pWp0 takes on the same connotation, but is used as an absolute noise level (weighted).

Digital Level Plan. The concept of transmission level point applies strictly to analog transmission. It has no real meaning in digital transmission, except where the signal is in analog form. Nevertheless, the concept of TLP is a powerful one, which can be retained.

In North America, when there is cutover to an all-digital network, a fixed transmission loss plan will be in place. The toll network will operate, end-to-end, with a 6-dB loss. A digital toll connecting trunk will have a 3-dB loss. There are two toll connecting trunks in a built-up toll connection, by definition. The remaining intervening toll trunks will operate at 0 dB loss/ 0 dB gain; thus the 6-dB total loss.

By the following, we can see that the 0 TLP concept still hangs on. We quote from

Telecommunication Transmission Engineering, Vol. 3 (AT&T, New York):

It is desirable in the fixed loss network to retain the 6-dB loss for test conditions so that all trunks have an EML (expected measured loss) of 6 dB. To accomplish this, the transmitting and receiving test equipment at digital offices (exchanges) must be equipped with 3-dB pads with analog-digital converters. Because of the use of 3-dB test pads, the No. 4 ESS (ATT digital toll exchange) can be considered at −3 TLP even though signals are in digital form. Since the path through the machine (digital switch) is lossless, the −3 TLP applies to the incoming as well as the outgoing side of the machine, a feature unique to digital switching machines.

C.11 dBi

The dBi is used to quantify the gain of an antenna. It stands for dB above (or below) an isotropic. If it is above, we will often use the plus (+) sign, and when below an isotropic, we will use a minus (−) sign. An isotropic is an imaginary reference antenna with uniform gain in all three dimensions. Thus, by definition, it has a gain of 1 dB or 0 dB. In this text, and in others dealing with commercial telecommunications, all antennas will have a “positive” gain. In other words, the gain will be greater than an isotropic. For example, parabolic dish antennas can display gains from 15 dBi to over 60 dBi.

C.11.1 dBd

The dBd is another dB unit used to measure antenna gain. The abbreviation dBd stands for dB relative to a dipole. This dB unit is widely used in cellular and PCS radio technology. When compared to an isotropic, the dBd unit has a 2.15-dB gain over an isotropic. For example, +2 dBd c +4.15 dBi.

REFERENCES 631

C.12 EIRP

EIRP stands for “effective isotropically radiated power.” We use the term to express how much transmitted power is radiated in the desired direction. The unit of measure is dBW or dBm, because we are talking about power.

EIRPdBW c Pt(dBW) + LL(dB) + antenna gain(dBi),

where Pt is the output power of the transmitter either in dBm or dBW. LL is the line loss in dB. That is the transmission line connecting the transmitter to the antenna. The third factor is the antenna gain in dB.

Warning! Most transmitters give the output power in watts. This value must be converted to dBm or dBW.

Example 1. A transmitter has an output of 20 W, the line loss is 2.5 dB, and the antenna has 27-dB gain. What is the EIRP in dBW?

Convert the 20 W to dBW c +13 dBW. Now we simply algebraically add:

EIRP c +13 dBW − 2.5 dB + 27 dB c +37.5 dBW.

Example 2. A transmitter has an output of 500 mW, the line losses are 5.5 dB, and the antenna gain is 39 dB. What is the EIRP in dBm?

Convert the transmitter output to dBm, which c +27 dBm. Now simply algebraically add [Ref. 3]:

EIRP c +27 dBm − 5.5 dB + 39 dB c 60.5 dBm.

REFERENCES

1. Transmission Systems for Communications, 5th ed., Bell Telephone Laboratories, Holmdel, NJ, 1982.

2. Transmission Systems for Communications, Revised 4th ed., Bell Telephone Laboratories, Merrimack Valley, MA, 1971.

3. R. L. Freeman, Telecommunications Transmission Handbook, 4th ed., Wiley, New York, 1998.

634 ACRONYMS AND ABBREVIATIONS