# Decibel is logarithmic unit

### Decibel

The decibel (dB) is generally used to measure sound levels and is also commonly used for signalling and communications, but it is predominantly is used in telecommunications, electronics and acoustics. The dB is a logarithmic unit used to describe a ratio. The ratio may be voltage, sound pressure, power, current or intensity etc. The dB is not a fixed quantity, it is a ratio of two quantities,for example when used to express power gain (Power gain2>Power gain1), or power loss (Power loss2<Power loss1) a negative number will be present with power loss.

The advantages of the dB are such as the ability to conveniently represent very large or small numbers, a logarithmic scaling that more or less corresponds to the human perception of sound and light, and the capability to carry out multiplication of ratios by simple addition and subtraction.

### Logarithms

The dBcomes from a logarithmic unit of measurement called a "Bel". One Bel is defined as a power ratio of ten (or ten times the power). The Bel is a large unit, so the decibel, which is 1/10 of a Bel, is more regularly used.

The decibel is expressed as the base10 logarithm of the ratio of the powers of two signals: dB = 10 log (Power1/Power2)

Signal amplitude can also be expressed in dB, because power is proportional to the square of a signal's amplitude, dB is expressed as follows: dB = 20 log (Amplitude1/Amplitude2).

Logarithms are helpful because signal power tends to span several orders of magnitude, and signal attenuation losses and gains can be expressed in terms of subtraction and addition.

### Milliwatt example

dBm is defined as power ratio in decibel (dB) referenced to one milliwatt (mW). It is an abbreviation for dB with respect to 1 mW and the "m" in dBm stands for milliwatt.

dBm is used differently from dB. dBm is absolute power and dB is the ratio of two values and is used to represent attenuation or gain. E.g., 3 dBm means 2 mW, and 3 dB means a gain of 2. Likewise, -3 dBm means 0.5 mW, whereas -3 dB means attenuation of 2.

### Voltage gain of an Op Amp

The core function of an operational amplifier is to amplify the input signal. The more open loop gain it has the better, so for an ideal amplifier the voltage gain will be infinite.

### Audio signal

The definition of dB sound pressure level is the 20 log of the ratio between the measured sound pressure level and always a reference point.

The softest sound a "normal" human ear can detect has a pressure variation of 20 micro Pascals, abbreviated as Pa, which is 20 x 10-6 Pa and is called the Threshold of Hearing. When dealing with hearing, the perceived loudness of a sound correlates roughly logarithmically to its sound pressure. Most measurements of audio equipment will be made relative to this level, meaning 1 pascal will equal 94 dB of sound pressure.

To express sound or noise in terms of Pa it is quite inconvenient because you have to deal with such a wide range of numbers. The more convenient way is to use a logarithmic scale for the loudness of noise or sound, using 10 as the base; the dB scale is therefore used.

Decibels are the logarithmic quantity used as the units of A-weighted sound pressure level. To assess noise, it is necessary to work out the increase or decrease in A-weighted sound pressure level, using the formula below.

### Signal-to-noise ratio

Because noise is very important, different types of measures have been developed to calculate the effect of noise on a communications system.

The measurement below is signal-to-noise ratio (SNR):

For nearly almost every application, it is more convenient to express SNR logarithmically, using dB:

E.g., if the noise power at the output of a receiver is 200 mW, and the signal power is 500 mW, the SNR is given by:

In order to accomplish reliable communications, the SNR should exceed a minimum value specific to each type of modulation and/or signal. E.g., AM voice transmissions are tricky to understand when the SNR drops below 10 dB and binary phase shift keying (BPSK) often becomes redundant when the SNR drops below 4 dB.

### Thermal noise

Thermal noise is formed by the movement of electrons in a resistor. Because the resistor is at a temperature above absolute zero (-459 F), the electrons move erratically in the solid. This random, fluctuating movement of electrons generates a noise voltage at the terminals of the resistor.

Another name for Thermal noise is also known as white noise this is because the amplitude of thermal noise is not reliant on frequency. As a result, thermal noise contains noise signals of all frequencies and all these signals have the same average amplitude. The noise voltage that appears across a resistor at temperature T is shown in the formula below:

k = Boltzmann's constant (1.38*10-23 J/K)

T = absolute temperature (degrees K)

B = bandwidth (Hz)

R = resistance (ohms)

The internal resistance of transistors, diodes, and other active electronic components creates thermal noise. For inductors and capacitors the internal resistances are slight and they can be considered to be noiseless.

Because of Johnson noise it is common to keep circuits for processing very low power signals, such as those found in radio telescopes at low temperatures.

### Cross-talk noise

Crosstalk is a phenomenon by which a signal transmitted on one circuit of a transmission system creates an undesired effect in another circuit. Crosstalk is usually caused by undesired inductive, capacitive, or conductive coupling from one circuit or part of a circuit to another.

In telecommunications crosstalk is often distinguishable as pieces of speech or signaling tones leaking from other people's connections. If the connection is analogue, twisted pair cabling can often be used to reduce crosstalk. Alternatively, the signals can be converted to digital form, which is much less susceptible to crosstalk.

In integrated circuit design, crosstalk normally refers to a signal affecting another nearby signal. Commonly the coupling is capacitive, and to the nearest neighbor, but other forms of coupling and effects on signal further away are sometimes important, especially in analogue designs. There are a wide variety of possible fixes, with increased spacing and shielding being the most common.

### Shot noise

Another "white noise" is shot noise. Shot noise normally occurs when there is a potential barrier (voltage differential). PN junction diode is an example that has a potential barrier. When the electrons and holes cross the barrier, shot noise is produced. Also noise is produced in active devices such as transistors. The flow of current in a transistor is not a smooth steady flow. The current flow is made of discrete current carriers, electrons, and the number of electrons leaving the collector of a transistor is not constant, but varies slightly from moment to moment. In bipolar transistors, the shot noise increases as the bias current is increased. In FET's, the shot noise does not change.

Diodes and vacuum tubes will all produce shot noise. But a resistor normally doesn't since there is no potential barrier built within a resistor. Current flowing through a resistor will not exhibit any fluctuations. However, current flowing through a diode produces small fluctuations. This is due to electrons arriving in quanta, one electron at a time. The current flow is not continuous, but limited by the quantum of the electron charges.

When a mean current I flows, Shot noise leads to current fluctuations given by

I2(f) = 2eI0A2/Hz Where, e (1.6 x 10-19 coulombs). Is the electronic charge.

Shot noise is proportional to the current passing through the devise.

### Class "A" amplifiers

A class "A" amplifier is biased to a point where plate current in all the output devices flows for the entire 360 degrees of the input cycle, at the full, unclipped output of the amplifier. This is typically done by biasing the output stage halfway between cut off and saturation, with the plate load impedance to an suitable value that gives maximum undistorted output power. This is the least efficient process of amplification, because the output devices are dissipating maximum power with no input signal.

Class "A" amplifiers frequently consist of a driven transistor connected from output to positive power supply and a constant current transistor connected from output to negative power supply. The signal to the driven transistor modulates the output voltage and the output current. With no input signal, the constant bias current flows directly from the positive supply to the negative supply, resulting in no output current, but lots of power consumed. Other Class "A" amps have both transistors driven in a push-pull fashion.

The leading advantage of a Class "A" amplifier is that it is most linear, i.e.: has the lowest distortion. There are advantages to push-pull class "A" amplification. Firstly, the bias current for each side is flowing in opposite directions in the primary of the output transformer, so they effectively cancel each other out. This lack of static, DC offset current in the output transformer means that the core can be made smaller, because it requires no air gap to prevent core saturation from the static DC offset current. A single-ended class "A" amplifier output transformer is huge compared to a push-pull class "A" amplifier of the same power level. The air gap required to prevent core saturation drastically reduces the primary inductance, so the transformer has to have a larger core and more windings to achieve the same primary inductance and the same -3dB lower frequency cut off point. Secondly, a push-pull class "A" amplifier output stage will have inherent rejection of power supply ripple and noise. This is because the power supply signal is "common-mode", i.e., it is amplified by each side equally, but because each side is out of phase, it cancels in the output.

One major disadvantage of a Class "A" amplifier is that it is inefficient, i.e.: it takes a very large Class "A" amplifier to deliver 60 watts, and that amplifier uses lots of electricity and gets very hot quickly. The main disadvantage of push-pull class "A" amplification over single-ended class "A" is the necessity for a phase splitter stage to generate the oppositely-phased drive signals.

### Class "B" amplifiers

Class "B" amplifiers consist of a driven transistor connected from output to positive power supply and another driven transistor connected from output to negative power supply. The signal drives one transistor on while the other is off, so in a Class "B" amplifier no power is wasted going from the positive supply straight to the negative supply.

A class "B" amplifier is one which the grid bias in all output tubesis set at cut off, i.e., no plate current flows in the absence of an input signal. Plate current only flows when a signal is present, and only flows for exactly half, or 180 degrees, of the input cycle.

For audio amplification purposes, a class "B" amplifier must operate in push-pull mode, because each output device only amplifies half the input signal, and the output would be fully clipped on one side if operated single-ended. It is important to remember that, even though the current in one side is fully off, or "clipped on one side", the output waveform is not clipped at all, because the other tube has taken over the job of reproducing it's half of the waveform.Clipping of the output stage will only happen when both tubes are at their respective, and opposite, limits of saturation and cut off.

The advantage of class "B" amplifiers operation is efficiency, which is far greater than the class "A", because the average dissipation of the output devices is much smaller, because they are biased normally "off", and only dissipate power during half the input cycle. The limiting factor in output power is the average dissipation of the output devices. If the average dissipation can be decreased, more output power can be obtained.

The disadvantage of class "B" amplifiers operation is a large amount of "crossover distortion", which occurs when one tube of the push-pull pair cuts off and the other turns on. The characteristic curves of a tube are not perfectly linear and symmetrical, so the "handoff" between the two sides results in a short time at the zero crossing where there is distortion. This crossover distortion looks like a notch, or flat spot, in the sine wave as it crosses the zero axis. There are almost no Class "B" amplifiers on the market today.

### Amplifier Feedback

Feedback is a term used in which a portion of the output is taken back to the input. Negative feedback is widely used in amplifier circuits as it reduces the gain. It also makes the amplifier more stable. Amplifiers without negative feedback tend to be rather unstable. This can arise due to:

• Temperature differences
• Stray inductance and capacitance effects
• Noise within the components or from poor soldering.
• Fluctuations from the power supply.

The effect of an unstable amplifier is that the output becomes distorted in an irregular and random way.

Reducing the gain when feeding back a negative signal from the output cancels part of the input signal but does have benefits, because:

• It helps to overcome distortion and non-linearity.
• It flattens frequency response or allows you to tailor it to a desired frequency response curve.
• It makes properties predictable, less dependent on temperature, manufacturing differences or other internal properties of the active device.
• Circuit properties are dependent upon the external feedback network and are thus easily controlled by external circuit elements.
• Circuit design can concentrate on function and not the details of operating point selection, biasing, and the other details characteristic of discrete transistor amplifier design.

### Stabilization of Voltage Gain

One of the benefits of negative feedback is the stabilization of the voltage gain of an amplifier against changes in the components. If you characterize the gain without feedback (the open loop gain) by A0 , then the system gain with negative feedback is

where B is the fraction of the output which feeds back as a negative voltage at the input. The extent of this stabilizing influence is shown below:

This stabilization increases the effective bandwidth.

### Increasing Input Impedance

The input impedance is which without negative feedback is Zin0. But with feedback, the current is reduced to

### Decreasing Output Impedance

As in the approach to input impedance, the effect of negative feedback on output impedance can be obtained by analysis of the equivalent circuit.

Things become more subtle here because the input voltage vin must be held constant while we see how vout varies with iout . The easiest way to do this is with the partial derivative.

### Decreasing Distortion with Feedback

The use of negative feedback can discriminate against sources of noise or distortion within an amplifier. Considering a two-stage amplifier with sources of distortion vd1 and vd2 inside the feedback loop.

The output voltage shows discrimination against the distortion voltages.

Distortion reduction takes the form below for this amplifier, showing that distortion within the feedback loop is discriminated against, with more reduction of distortion which arises near the output.

### Increasing the Bandwidth

Amplifier gain will generally decrease at higher frequencies, but the contribution of negative feedback in stabilizing voltage gain and making it nearly independent of the open-loop gain is a major contribution to extending the useful frequency range of amplifiers.

The input impedance is which without negative feedback is Zin0. But with feedback, the current is reduced to

### Resources

• www.phys.unsw.edu.au
• http://www.aubraux.com/design/milli-watts-to-dbm-calculator.php
• http://www.electronics-tutorials.ws/opamp/opamp_1.html
• www.wikipedia.org
• http://www.ycars.org/EFRA/Module%20B/noise.htm
• http://stason.org/TULARC/entertainment/audio/general/11-18-What-is-Amplifier-Class-A-What-is-Class-B-What-is-Cl.html
• http://www.aikenamps.com/ClassA.htm
• http://hyperphysics.phy-astr.gsu.edu/hbase/Electronic/feedn2.html#c1

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