Intermediate Frequency and Images
The choice of IF is usually a design compromise. The primary objective is to obtain good selectivity. Narrowband selectivity is best obtained at lower frequencies, particularly when conventional LC tuned circuits are used. Even active RC filters can be used when IFs of 500 KHz or less are used. There are various design benefits of using a low IF.
At low frequencies, the circuits are far more stable with high gain. At higher frequencies, circuit layouts must take into account stray inductances and capacitances, as well as the need for shielding, if undesired feedback paths are to be avoided. With very high circuit gain, some of the signal can be fed back in phase and cause oscillation.
Oscillation is not as much of a problem at lower frequencies. However, when low IFs are selected, a different sort of problem is faced, particularly if the signal to be received is very high in frequency. This is the problem of images. An image is a potentially interfering RF signal that is spaced from the desired incoming signal by a frequency that is two times the intermediate frequency above or below the incoming frequency, or
fi=fs+ 2fIF and fi = fs – 2fIF
where fi = image frequency
fs = desired signal frequency
fIF = intermediate frequency
This is illustrated graphically in Fig. 9-15. Note that which of the images occurs depends on whether the local oscillator frequency fo is above or below the signal frequency.
Frequency Relationships and Images
As stated previously, the mixer in a superheterodyne receiver produces the sum and difference frequencies of the incoming signal and the local oscillator signal. Normally, the difference frequency is selected as the IF. The frequency of the local oscillator is usually chosen to be higher in frequency than the incoming signal by the IF.
However, the local oscillator frequency could also be made lower than the incoming signal frequency by an amount equal to the IF. Either choice will produce the desired difference frequency. For the following example, assume that the local oscillator frequency is higher than the incoming signal frequency.
Now, if an image signal appears at the input of the mixer, the mixer will, of course, produce the sum and difference frequencies regardless of the inputs. Therefore, the mixer output will again be the difference frequency at the IF value. Assume, e.g., the desired signal frequency of 90 MHz and a local oscillator frequency of 100 MHz. The IF is the difference 100 – 90 = 10 MHz. The image frequency is fi=fs+ 2fIF= 90 + 2(10) = 90 +20 = 110 MHz.
If an undesired signal, the image, appears at the mixer input, the output will be the difference 110 – 100 = 10 MHz. The IF amplifier will pass it. Now, look at Fig. 9-16, which shows the relationships between the signal, local oscillator, and image frequencies. The mixer produces the difference between the local oscillator frequency and the desired signal frequency, or the difference between the local oscillator frequency and the image frequency. In both cases, the IF is 10 MHz. This means that a signal spaced from the desired signal by two times the IF can also be picked up by the receiver and converted to the IF. When this occurs, the image signal interferes with the desired signal. In today’s crowded RF spectrum, chances are high that there will be a signal on the image frequency, and image interference can even make the desired signal unintelligible. The superheterodyne design must, therefore, find a way to solve the image problem.
Solving the Image Problem
Image interference occurs only when the image signal is allowed to appear at the mixer input. This is the reason for using high-Q tuned circuits ahead of the mixer or a selective RF amplifier. If the selectivity of the RF amplifier and tuned circuits is good enough, the image will be rejected. In a fixed tuned receiver designed for a specific frequency, it is possible to optimize the receiver front end for the good selectivity necessary to eliminate images. But many receivers have broadband RF amplifiers that allow many frequencies within a specific band to pass. Other receivers must be made tunable over a wide frequency range. In such cases, selectivity becomes a problem.
Assume, e.g., that a receiver is designed to pick up a signal at 25 MHz. The IF is 500 kHz, or 0.5 MHz. The local oscillator is adjusted to a frequency right above the incoming signal by an amount equal to the IF, or 25 + 0.5 = 25.5 MHz. When the local oscillator and signal frequencies are mixed, the difference is 0.5 MHz, as desired.
The image frequency is fi = fs + 2fIF = 25 + 2(0.5) = 26 MHz. An image frequency of 26 MHz will cause interference to the desired signal at 25 MHz unless it is rejected. The signal, local oscillator, and image frequencies for this situation are shown in Fig. 9-17. Now, assume that a tuned circuit ahead of the mixer has a Q of 10. Given this and the resonant frequency, the bandwidth of the resonant circuit can be calculated as BW = fr/Q = 25/10 = 2.5 MHz.
The response curve for this tuned circuit is shown in Fig. 9-17. As shown, the bandwidth of the resonant circuit is relatively wide. The bandwidth is centered on the signal frequency of 25 MHz. The upper cutoff frequency is f2 = 26.25 MHz, the lower cutoff frequency is f1 = 23.75 MHz, and the bandwidth is BW = f2 – f1 = 26.25 – 23.75 = 2.5 MHz. (Remember that the bandwidth is measured at the 3-dB down points on the tuned circuit response curve.)
The fact that the upper cutoff frequency is higher than the image frequency, 26 MHz, means that the image frequency appears in the passband; it would thus be passed relatively unattenuated by the tuned circuit, causing interference.
passed relatively unattenuated by the tuned circuit, causing interference. It is clear how cascading tuned circuits and making them with higher Qs can help solve the problem. For example, assume a Q of 20, instead of the previously given value of 10. The bandwidth at the center frequency of 25 MHz is then fs/Q = 25/20 = 1.25 MHz.
The resulting response curve is shown by the darker line in Fig. 9-17. The image is now outside of the passband and is thus attenuated. Using a Q of 20 would not solve the image problem completely, but still higher Qs would further narrow the bandwidth, attenuating the image even more.
Higher Qs are, however, difficult to achieve and often complicate the design of receivers that must be tuned over a wide range of frequencies. The usual solution to this problem is to choose a higher IF. Assume, e.g., that an intermediate frequency of 9 MHz is chosen (the Q is still 10). Now the image frequency is fi = 25 + 2(9) = 43 MHz. A signal at a 43-MHz frequency would interfere with the desired 25-MHz signal if it were allowed to pass into the mixer. But 43 MHz is well out of the tuned circuit bandpass; the relatively low-Q selectivity of 10 is sufficient to adequately reject the image. Of course, choosing the higher intermediate frequency causes some design difficulties, as indicated earlier.
To summarize, the IF is made as high as possible for effective elimination of the image problem, yet low enough to prevent design problems. In most receivers, the IF varies in proportion to the frequencies that must be covered. At low frequencies, low values of IF are used. A value of 455 kHz is common for AM broadcast band receivers and for others covering that general frequency range. At frequencies up to about 30 MHz, 3385 kHz and 9 MHz are common IF frequencies. In FM radios that receive 88 to 108 MHz, 10.7 MHz is a standard IF. In TV receivers, an IF in the 40- to the 50-MHz range is common. In the microwave region, radar receivers typically use an IF in the 60-MHz range, and satellite communication equipment uses 70- and 140-MHz IFs.
Another way to obtain selectivity while eliminating the image problem is to use a dual-conversion superheterodyne receiver. See Fig. 9-18. The receiver shown in the figure uses two mixers and local oscillators, and so it has two IFs. The first mixer converts the incoming signal to a relatively high intermediate frequency for the purpose of eliminating the images; the second mixer converts that IF down to a much lower frequency, where good selectivity is easier to obtain.
Fig. 9-18 shows how the different frequencies are obtained. Each mixer produces a different frequency. The first local oscillator is variable and provides the tuning for the receiver. The second local oscillator is fixed in frequency. Since it needs to convert only one fixed IF to a lower IF, this local oscillator does not have to be tunable. In most cases, its frequency is set by a quartz crystal. In some receivers, the first mixer is driven by the fixed-frequency local oscillator, and tuning is done with the second local oscillator. Dual-conversion receivers are relatively common. Most shortwave receivers and many at VHF, UHF, and microwave frequencies use dual conversion. For example, a CB receiver operating in the 27-MHz range typically uses a 10.7-MHz first IF and a 455-kHz second
IF. For some critical applications, triple-conversion receivers are used to further minimize the image problem, although their use is not common. A triple-conversion receiver uses three mixers and three different intermediate-frequency values.
A superheterodyne receiver must cover the range from 220 to 224 MHz. The first IF is 10.7 MHz; the second is 1.5 MHz. Find (a) the local oscillator tuning range, (b) the frequency of the second local oscillator, and (c) the first IF image frequency range. (Assume a local oscillator frequency higher than the input by the IF.)
Direct Conversion Receivers
A special version of the superheterodyne is known as the direct conversion (DC) or zeroIF (ZIF) receiver. Instead of translating the incoming signal to another (usually lower) intermediate frequency, dc receivers convert the incoming signal directly to the baseband. In other words, they perform the demodulation of the signal as part of the translation.
Fig. 9-19 shows the basic ZIF receiver architecture. The low-noise amplifier (LNA) boosts the signal level before the mixer. The local oscillator (LO) frequency, usually from a PLL frequency synthesizer fLO, is set to the frequency of the incoming signal fs.
fLO = fs
The sum and difference frequencies as a result of mixing are
fLO – fs = 0
fLO + fs = 2fLO = 2fs
The difference frequency is zero. Without modulation, there is no output. With AM, the sidebands mix with the LO to reproduce the original modulation baseband signal. In this instance, the mixer is also the demodulator. The sum is twice the LO frequency that is removed by the low-pass filter (LPF).
Assume a carrier of 21 MHz and a voice modulation signal from 300 to 3000 Hz and AM. The sidebands extend from 20,997,000 to 21,003,000 Hz. At the receiver, the LO is set to 21 MHz. The mixer produces
21,000,000 – 20,997,000 = 3000 Hz
21,003,000 – 21,000,000 =3000 Hz
21,000,000 + 21,003,000 = 42,003,000 Hz
21,000,000 + 20,997,000 = 41,997,000 Hz
A low-pass filter at the mixer output whose cutoff frequency is set to 3 kHz easily filters out the 42-MHz components.
The DC receiver has several key benefits. First, no separate IF filter is needed. This is usually a crystal, ceramic, or SAW filter that is expensive and takes up valuable printed circuit board space in compact designs. An inexpensive RC, LC, or the active low-pass filter at the mixer output supplies the needed selectivity. Second, no separate detector circuit is needed, because demodulation is inherent in the technique. Third, in transceivers that use half-duplex and in which the transmitter and receiver are on the same frequency, only one PLL frequency synthesizer voltage-controlled oscillator is needed. All these benefits result in simplicity and its attendant lower cost. Fourth, there is no image problem.
The disadvantages of this receiver are subtle. In designs with no RF amplifier (LNA), the LO signal can leak through the mixer to the antenna and radiate. A LNA reduces this likelihood, but even so, careful design is required to minimize the radiation. Second, an undesired dc offset can develop in the output. Unless all circuits are perfectly balanced, the dc offset can upset bias arrangements in later circuits as well as cause circuit saturation that will prevent the amplification and other operations. Finally, the ZIF receiver can be used only with CW, AM, SSB, or DSB. It cannot recognize phase or frequency variations. To use this type of receiver with FM, FSK, PM, or PSK, or any form of digital modulation, two mixers are required along with a quadrature LO arrangement. Such designs are used in most cell phones and other wireless receivers.
Fig. 9-20 shows a direct conversion receiver that is typical of those using digital modulation. the incoming signal is sent to a SAW filter that provides some initial selectivity. The LNA provides amplification. The LNA output is fed to two mixers. The local oscillator (LO) signal, usually from a synthesizer, is fed directly to the upper mixer (sin θ) and to a 90° phase shifter that, in turn, supplies the lower mixer (cos θ). Remember, the LO frequency is equal to the incoming signal frequency. The mixers provide baseband signals at their outputs. The double LO frequency signals resulting from mixing are removed with the low-pass filters (LPFs). The two baseband signals are separated in phase by 90°. The upper signal is usually referred to as the in-phase I signal while the lower signal is referred to as the quadrature Q signal.
(Quadrature means a 90° phase difference.) The I and Q signals are then sent to analog-to-digital converters (ADCs) where they are converted to binary signals. The binary signals are then sent to a digital signal processor (DSP). The DSP contains a prestored subroutine that performs the demodulation. This algorithm requires the two quadrature signals in order to have enough data to distinguish phase and frequency changes in the original signal resulting from modulation. The output from the demodulation subroutine is fed to an external digital-to-analog converter (DAC) where the original modulating signal is reproduced. This I-Q direct conversion architecture is now one of the most common receiver architectures used in cell phones and wireless networking ICs.
Low IF Receiver
An alternative to a direct conversion receiver is the low IF receiver. This design is used to mitigate or eliminate the LO leakage and dc output problems. The resulting receiver is still superheterodyne, but using a low IF offers other benefits such as simpler filters.
What is a low IF? It depends upon the operating frequency. Early cell phone designs used an IF in the 125 kHz range, making it possible to use simple on-chip RC filters. In other designs, a low IF may be in the 1 or 2 MHz range if the operating frequency is above 1 GHz.
A software-defined radio (SDR) is a receiver in which most of the functions are performed by a digital signal processor. Fig. 9-21 is a general block diagram of an SDR. While only one mixer and ADC are shown, keep in mind that the I and Q architecture of Fig. 9-20 is normally used. As in most receivers, a LNA provides initial amplification and a mixer down-converts the signal to an IF or to baseband in a DC receiver. The IF or baseband signal is then digitized by an analog-to-digital (A/D) converter. The binary words representing the IF signal with its modulation are stored in RAM. A DSP chip then performs additional filtering, demodulation, and baseband operations (voice decoding, companding, etc.).
The fastest A/D converters available today can digitize at a rate of up to 300 MHz. To meet the Nyquist requirement, this means that the highest frequency that can be digitized is less than 150 MHz. This is why the SDR must down-convert the incoming signal to an IF of less than 150 MHz. Further, the DSP must be fast enough to perform the DSP math in real-time. Although DSP chips can operate at clock rates up to 1 GHz, the time it takes to execute even at these speeds limits the IF to a lower value. A practical value is in the 40- to the 90-MHz range, where the A/D converter and the DSP can handle the computing chores.
An alternative is to use a dual-conversion SDR. The first mixer converts the signal to an IF that is then fed to the A/D converter, where it digitizes the data. The DSP chip is then used to down-convert the signal to an even lower IF. This mixing or down-conversion is done digitally. It is similar to the process of aliasing, in which a lower difference frequency is generated. From there the DSP performs the filtering and demodulation duties. Today, most IC receiver designs are similar to that shown in Fig. 9-20. For some designs, the critical ADC sampling frequency can be lowered using undersampling techniques as described.
The filtering, demodulation, and other processes are, of course, defined by mathematical algorithms that are in turn programmed with a computer language. The resulting programs are stored in the DSP ROM.
SDR techniques have been known for many years, but only since the early to mid-1990s have A/D converter circuits and DSP chips become fast enough to perform the desired operations at radio frequencies. SDRs have already been widely adopted in military receivers, cell phones, and cell phone base stations. As prices continue to drop and as A/D converters become even faster, these methods will become even more widely used in other communication equipment.
The benefits of SDRs are improved performance and flexibility. DSP filtering and other processes are typically superior to equivalent analog techniques. Furthermore, the receiver characteristics (type of modulation, selectivity, etc.) can be easily changed by running a different program. SDRs can be changed by downloading or switching to a new processing program that the DSP can execute. No hardware changes are required.
As A/D converters and DSPs get faster, it is expected that more receiver functions will become software-defined. The ultimate SDR is a LNA connected to an antenna and whose output goes directly to a fast A/D converter. All mixing, filtering, demodulation, and other operations are performed in DSP software.
Cognitive radio is the term describing an advanced form of SDR that is designed to help alleviate the frequency spectrum shortage. While most of the usable frequency spectrum has already been assigned by the various government regulating agencies, at any given time much of that spectrum goes unused, at least for part of the time. The question is, How can that spectrum be more efficiently assigned and used? A good example is the frequency spectrum assigned to the UHF TV stations. This spectrum in the 500- to the 800-MHz range is essentially vacant except for the occasional UHF TV station. Few people watch UHF TV directly by radio. Instead, most watch by cable, satellite, or Internet TV, which may retransmit the UHF TV station. This is a huge waste of precious spectrum space, yet broadcasters are reluctant to give it up. The cell phone companies, which are perpetually short of spectrum for new subscribers, covet this unused but unattainable space.
A cognitive radio is designed to seek out unused spectrum space and then reconfigure itself to receive and transmit on unused portions of the spectrum that it finds. Such radios are now possible because of the availability of very agile and wide-ranging frequency synthesizers and DSP techniques. The radio could easily change frequency as well as modulation/ multiplexing methods on the fly to establish communications. Consumer, military, and government service radios are now beginning to take advantage of these techniques. will discuss a specific case of cognitive radio called “white space” radio.
Noise is an electronic signal that is a mixture of many random frequencies at many amplitudes that gets added to a radio or information signal as it is transmitted from one place to another or as it is processed. Noise is not the same as interference from other information signals.
When you turn on any AM, FM, or shortwave receiver and tune it to some position between stations, the hiss or static that you hear in the speaker is noise. Noise also shows up on a black-and-white TV screen as snow or on a color screen as confetti. If the noise level is high enough and/or the signal is weak enough, the noise can completely obliterate the original signal. The noise that occurs in transmitting digital data causes bit errors and can result in information being garbled or lost.
The noise level in a system is proportional to temperature and bandwidth, and to the amount of current flowing in a component, the gain of the circuit, and the resistance of the circuit. Increasing any of these factors increases noise. Therefore, low noise is best obtained by using low-gain circuits, low direct current, low resistance values, and narrow bandwidths. Keeping the temperature low can also help.
Noise is a problem in communication systems whenever the received signals are very low in amplitude. When the transmission is over short distances or high-power transmitters are being used, noise is not usually a problem. But in most communication systems, weak signals are normal, and noise must be taken into account at the design stage. It is in the receiver that noise is the most detrimental because the receiver must amplify the weak signal and recover the information reliably.
Noise can be external to the receiver or originate within the receiver itself. Both types are found in all receivers, and both affect the SNR.
The signal-to-noise (S/N) ratio, also designated SNR, indicates the relative strengths of the signal and the noise in a communication system. The stronger the signal and the weaker the noise, the higher the S/N ratio. If the signal is weak and the noise is strong, the S/N ratio will be low and reception will be unreliable. Communication equipment is designed to produce the highest feasible S/N ratio.
Signals can be expressed in terms of voltage or power. The S/N ratio is computed by using either voltage or power values:
S/N = Vs/Vn
or S/N = Ps/Pn
where Vs = signal voltage
Vn = noise voltage
Ps = signal power
Pn = noise power
Assume, e.g., that the signal voltage is 1.2 μV and the noise is 0.3 μV. The S/N ratio is 1.2/0.3 = 4. Most S/N ratios are expressed in terms of power rather than voltage. For example, if the signal power is 5 μW and the power is 125 nW, the S/N ratio is 5 x 10-6/125 x 10-9 = 40.
The preceding S/N values can be converted to decibels as follows:
For voltage: dB = 20 log S/N = 20 log 4 = 20(0.602) = 12 dB
For power: dB = 10 log S/N = 10 log 40 =10(1.602) = 16 dB
However, it is expressed, if the S/N ratio is less than 1, the dB value will be negative and the noise will be stronger than the signal.
External noise comes from sources over which we have little or no control— industrial, atmospheric, or space. Regardless of its source, noise shows up as a random ac voltage and can be seen on an oscilloscope. The amplitude varies over a wide range, as does the frequency. One can say that noise, in general, contains all frequencies, varying randomly. This is generally known as white noise.
Atmospheric noise and space noise are a fact of life and simply cannot be eliminated. Some industrial noise can be controlled at the source, but because there are so many sources of this type of noise, there is no way to eliminate it. The key to reliable communication, then, is simply to generate signals at a high enough power to overcome external noise. In some cases, shielding sensitive circuits in metallic enclosures can aid in noise control.
Industrial noise is produced by manufactured equipment, such as automotive ignition systems, electric motors, and generators. Any electrical equipment that causes high voltages or currents to be switched produces transients that create noise. Noise pulses of large amplitude occur whenever a motor or other inductive device is turned on or off. The resulting transients are extremely large in amplitude and rich in random harmonics. Fluorescent and other forms of gas-filled lights are another common source of industrial noise.
The electrical disturbances that occur naturally in the earth’s atmosphere are another source of noise. Atmospheric noise is often referred to as static. Static usually comes from lightning, the electric discharges that occur between clouds or between the earth and clouds. Huge static charges build upon the clouds, and when the potential difference is great enough, an arc is created and electricity literally flows through the air. Lightning is very much like the static charges that we experience during a dry spell in the winter. The voltages involved are, however, enormous, and these transient electric signals of megawatt power generate harmonic energy that can travel over extremely long distances.
Like industrial noise, atmospheric noise shows up primarily as amplitude variations that add to a signal and interfere with it. Atmospheric noise has its greatest impact on signals at frequencies below 30 MHz.
Extraterrestrial noise, solar and cosmic, comes from sources in space. One of the primary sources of extraterrestrial noise is the sun, which radiates a wide range of signals in a broad noise spectrum. The noise intensity produced by the sun varies with time. In fact, the sun has a repeatable 11-year noise cycle. During the peak of the cycle, the sun produces an awesome amount of noise that causes tremendous radio signal interference and makes many frequencies unusable for communication. During other years, the noise is at a lower level.
Noise generated by stars outside our solar system is generally known as cosmic noise. Although its level is not as great as that of noise produced by the sun, because of the great distances between those stars and earth, it is nevertheless an important source of noise that must be considered. It shows up primarily in the 10-MHz to 1.5-GHz range, but causes the greatest disruptions in the 15- to 150-MHz range.
Electronic components in a receiver such as resistors, diodes, and transistors are major sources of internal noise. Internal noise, although it is low level, is often great enough to interfere with weak signals. The main sources of internal noise in a receiver are thermal noise, semiconductor noise, and intermodulation distortion. Since the sources of internal noise are well known, there is some design control over this type of noise.
Most internal noise is caused by a phenomenon known as thermal agitation, the random motion of free electrons in a conductor caused by heat. Increasing the temperature causes this atomic motion to increase. Since the components are conductors, the movement of electrons constitutes a current fl ow that causes a small voltage to be produced across that component. Electrons traversing a conductor as current flows experience fleeting impediments in their path as they encounter the thermally agitated atoms. The apparent resistance of the conductor thus fluctuates, causing the
thermally produced random voltage we call noise.
You can actually observe this noise by simply connecting a high-value (megohm) resistor to a very high-gain oscilloscope. The motion of the electrons due to room temperature in the resistor causes a voltage to appear across it. The voltage variation is completely random and at a very low level. The noise developed across a resistor is proportional to the temperature to which it is exposed.
Thermal agitation is often referred to as white noise or Johnson noise, after J. B. Johnson, who discovered it in 1928. Just as white light contains all other light frequencies, white noise contains all frequencies randomly occurring at random amplitudes. A white noise signal, therefore, occupies, theoretically at least, infinite bandwidth. Filtered or band-limited noise is referred to as pink noise.
In a relatively large resistor at room temperature or higher, the noise voltage across it can be as high as several microvolts. This is the same order of magnitude as or higher than that of many weak RF signals. Weaker-amplitude signals will be totally masked by this noise.
Since noise is a very broadband signal containing a tremendous range of random frequencies, its level can be reduced by limiting the bandwidth. If a noise signal is fed into a selective tuned circuit, many of the noise frequencies are rejected and the overall noise level goes down. The noise power is proportional to the bandwidth of any circuit to which it is applied. Filtering can reduce the noise level, but does not eliminate it entirely.
The amount of open-circuit noise voltage appearing across a resistor or the input impedance to a receiver can be calculated according to Johnson’s formula
where υn = rms noise voltage
k = Boltzman’s constant (1.38 x 10-23 J/K)
T = temperature, K (°C + 273)
B = bandwidth, Hz
R = resistance, Ω
The resistor is acting as a voltage generator with an internal resistance equal to the resistor value. See Fig. 9-22. Naturally, if a load is connected across the resistor generator, the voltage will decrease as a result of voltage divider action.
What is the open-circuit noise voltage across a 100-kV resistor over the frequency range of direct current to 20 kHz at room temperature (25°C)?
The bandwidth of a receiver with a 75-V input resistance is 6 MHz. The temperature is 29°C. What is the input thermal noise voltage?
Since noise voltage is proportional to resistance value, temperature, and bandwidth, noise voltage can be reduced by reducing resistance, temperature, and bandwidth or any combination to the minimum level acceptable for the given application. In many cases, of course, the values of resistance and bandwidth cannot be changed. One thing, however, that is always controllable to some extent is temperature. Anything that can be done to cool the circuits will greatly reduce the noise. Heat sinks, cooling fans, and good ventilation can help lower noise. Many low-noise receivers for weak microwave signals from spacecraft and in radio telescopes are supercooled; i.e., their temperature is reduced to very low (cryogenic) levels with liquid nitrogen or liquid helium.
Thermal noise can also be computed as a power level. Johnson’s formula is then
Pn = kTB
where Pn is the average noise power in watts.
Note that when you are dealing with power, the value of resistance does not enter into the equation.
What is the average noise power of a device operating at a temperature of 90°F with a bandwidth of 30 kHz?
Electronic components such as diodes and transistors are major contributors of noise. In addition to thermal noise, semiconductors produce shot noise, transit-time noise, and flicker noise
The most common type of semiconductor noise is shot noise. The current flow in any device is not direct and linear. The current carriers, electrons or holes, sometimes take random paths from source to destination, whether the destination is an output element, tube plate, or collector or drain in a transistor. It is this random movement that produces the shot effect. Shot noise is also produced by the random movement of electrons or holes across a PN junction. Even though current flow is established by external bias voltages, some random movement of electrons or holes will occur as a result of discontinuities in the device. For example, the interface between the copper lead and the semiconductor material forms a discontinuity that causes random movement of the current carriers.
Shot noise is also white noise in that it contains all frequencies and amplitudes over a very wide range. The amplitude of the noise voltage is unpredictable, but it does follow a Gaussian distribution curve that is a plot of the probability that specific amplitudes will occur. The amount of shot noise is directly proportional to the amount of dc bias flowing in a device. The bandwidth of the device or circuit is also important. The rms noise current in a device In is calculated with the formula
where q = charge on an electron, 1.6 x 10-19 C
I = direct current, A
B = bandwidth, Hz
As an example, assume a dc bias of 0.1 mA and a bandwidth of 12.5 kHz. The noise current is
Now assume that the current is flowing across the emitter-base junction of a bipolar transistor. The dynamic resistance of this junction re¿ can be calculated with the expression re‘ = 0.025/Ie, where Ie is the emitter current. Assuming an emitter current of 1 mA, we have re‘= 0.025/0.001 = 25 V. The noise voltage across the junction is found with Ohm’s law:
υn = In re‘ = 0.623 x 10-9 x 25 = 15.8 x 10-9V = 15.8 nV
This amount of voltage may seem negligible, but keep in mind that the transistor has gain and will therefore amplify this variation, making it larger in the output. Shot noise is normally lowered by keeping the transistor currents low since the noise current is proportional to the actual current. This is not true of MOSFETs, in which shot noise is relatively constant despite the current level.
Another kind of noise that occurs in transistors is called transit-time noise. The term transit time refers to how long it takes for a current carrier such as a hole or electron to move from the input to the output. The devices themselves are very tiny, so the distances involved are minimal, yet the time it takes for the current carriers to move even a short distance is finite. At low frequencies, this time is negligible; but when the frequency of operation is high and the period of the signal being processed is the same order of magnitude as the transit time, problems can occur. Transit-time noise shows up as a kind of random variation of current carriers within a device, occurring near the upper cutoff frequency. Transit-time noise is directly proportional to the frequency of operation. Since most circuits are designed to operate at a frequency much less than the transistor’s upper limit, transit-time noise is rarely a problem.
A third type of semiconductor noise, flicker noise or excess noise, also occurs in resistors and conductors. This disturbance is the result of minute random variations of resistance in the semiconductor material. It is directly proportional to current and temperature. However, it is inversely proportional to frequency, and for this reason it is sometimes referred to as 1/f noise. Flicker noise is highest at the lower frequencies and thus is not pure white noise. Because of the dearth of high-frequency components, 1/f noise is also called pink noise.
At some low frequencies, flicker noise begins to exceed thermal and shot noise. In some transistors, this transition frequency is as low as several hundred hertz; in others, the noise may begin to rise at a frequency as high as 100 kHz. This information is listed on the transistor datasheet, the best source of noise data
The amount of flicker noise present in resistors depends on the type of resistor. Fig. 9-23 shows the range of noise voltages produced by the various types of popular resistor types. The figures assume a common resistance, temperature, and bandwidth. Because carbon-composition resistors exhibit an enormous amount of flicker noise—an order of magnitude more than that of the other types—they are avoided in low-noise amplifiers and other circuits. Carbon and metal film resistors are much better, but metal film resistors may be more expensive. Wire-wound resistors have the least flicker noise but are rarely used because they contribute a large inductance to the circuit, which is unacceptable in RF circuits.
Fig. 9-24 shows the total noise voltage variation in a transistor, which is a composite of the various noise sources. At low frequencies, noise voltage is high, because of 1/f noise. At very high frequencies, the rise in noise is due to transit-time effects near the upper cutoff frequency of the device. Noise is lowest in the midrange, where most devices operate. The noise in this range is due to thermal and shot effects, with shot noise sometimes contributing more than thermal noise.
Intermodulation distortion results from the generation of new signals and harmonics caused by circuit nonlinearities. As stated previously, circuits can never be perfectly linear, and if bias voltages are incorrect in an amplifier or it is driven into clipping, it is likely to be more nonlinear than intended. Nonlinearities produce modulation or heterodyne effects. Any frequencies in the circuit mix together, forming sum and difference frequencies. When many frequencies are involved, or with pulses or rectangular waves, the large number of harmonics produces an even larger number of sum and difference frequencies.
When two signals are near the same frequency, some new sum and difference frequencies are generated by a nonlinearity, and they can appear inside the bandwidth of the amplifier. In most cases, such signals cannot be filtered out. As a result, they become interfering signals to the primary signals to be amplified. They are a form of noise.
Fig. 9-25 illustrates this. Signals f1 and f2 appear within the bandwidth of an amplifier. Any nonlinearity generates new signals f1 – f2 and f1 + f2. In addition, these new signals begin to mix with some of the harmonics generated by the nonlinearity (2f1, 2f2, 3f1, 3f2, etc.). Some of these new signals will occur within the amplifier bandpass.
Those new signals that cause the most trouble are the so-called third-order products, specifically 2f1 ± f2 and 2f2 ± f1. See the fi gure. Those most likely to be in the amplifier bandwidth are 2f1 – f2 and 2f2 – f1. These are the third-order products. The key to minimizing these extraneous intermodulation products is to maintain good linearity through biasing and input signal level control.
The resulting IMD products are small in amplitude but can be large enough to constitute a disturbance that can be regarded as a type of noise. This noise, which is not white or pink, can be predicted because the frequencies involved in generating the intermodulation products are known. Because of the predictable correlation between the known frequencies and the noise, intermodulation distortion is also called correlated noise. Correlated noise is produced only when signals are present. The types of noise discussed earlier are sometimes referred to as uncorrelated noise. Correlated noise is manifested as the low-level signals called birdies. It can be minimized by good design.
Expressing Noise Levels
The noise quality of a receiver can be expressed in terms of noise figure, noise factor, noise temperature, and SINAD.
Noise Factor and Noise Figure
The noise factor is the ratio of the S/N power at the input to the S/N power at the output. The device under consideration can be the entire receiver or a single amplifier stage. The noise factor or noise ratio (NR) is computed with the expression
When the noise factor is expressed in decibels, it is called the noise figure (NF):
NF = 10 log NR dB
Amplifiers and receivers always have more noise at the output than at the input because of the internal noise, which is added to the signal. And even as the signal is being amplified along the way, the noise generated in the process is amplified along with it. The S/N ratio at the output will be less than the S/N ratio of the input, and so the noise figure will always be greater than 1. A receiver that contributed no noise to the signal would have a noise figure of 1, or 0 dB, which is not attainable in practice. A transistor amplifier in a communication receiver usually has a noise figure of several decibels. The lower the noise figure, the better the amplifier or receiver. Noise figures of
less than about 2 dB are excellent.
An RF amplifier has an S/N ratio of 8 at the input and an S/N ratio of 6 at the output. What are the noise factor and noise figure?
NR = 8/6 = 1.333
NF = 10 log 1.3333 = 10 (0.125) = 1.25 dB
Most of the noise produced in a device is thermal noise, which is directly proportional to temperature. Therefore, another way to express the noise in an amplifier or receiver is in terms of noise temperature TN. Noise temperature is expressed in kelvins. Remember that the Kelvin temperature scale is related to the Celsius scale by the relationship TK = TC + 273. The relationship between noise temperature and NR is given by
TN = 290(NR – 1)
For example, if the noise ratio is 1.5, the equivalent noise temperature is TN = 290(1.5 – 1) = 290(0.5) = 145 K. Clearly, if the amplifier or receiver contributes
A receiver with a 75-V input resistance operates at a temperature of 31°C. The received signal is at 89 MHz with a bandwidth of 6 MHz. The received signal voltage of 8.3 μV is applied to an amplifier with a noise figure of 2.8 dB. Find (a) the input noise power, (b) the input signal power, (c) S/N, in decibels, (d) the noise factor and S/N of the amplifier, and (e) the noise temperature of the amplifier.
no noise, then NR will be 1, as indicated before. Plugging this value into the expression above gives an equivalent noise temperature of 0 K:
TN = 290 (1 – 1) 5=290 (0) = 0 K
the noise ratio is greater than 1, an equivalent noise temperature will be produced. The equivalent noise temperature is the temperature to which a resistor equal in value to Zo of the device would have to be raised to generate the same Vn as the device generates.
Noise temperature is used only in circuits or equipment that operates at VHF, UHF, or microwave frequencies. The noise factor or noise figure is used at lower frequencies. A good low-noise transistor or amplifier stage typically has a noise temperature of less than 100 K. The lower the noise temperature, the better the device. Often you will see the noise temperature of a transistor given in the datasheet.
Another way of expressing the quality and sensitivity of communication receivers is SINAD—the composite signal plus the noise and distortion divided by noise and distortion contributed by the receiver. In symbolic form,
Distortion refers to the harmonics present in a signal caused by nonlinearities. The SINAD ratio is also used to express the sensitivity of a receiver. Note that the SINAD ratio makes no attempt to discriminate between or to separate noise and distortion signals.
To obtain the SINAD ratio, an RF signal modulated by an audio signal (usually of 400 Hz or 1 kHz) is applied to the input of an amplifier or a receiver. The composite output is then measured, giving the S + N + D figure. Next, a highly selective notch (band-reject) filter is used to eliminate the modulating audio signal from the output, leaving the noise and distortion, or N + D.
The SINAD is a power ratio, and it is almost always expressed in decibels:
SINAD is the most often used measure of sensitivity for FM receivers used in two-way radios. It can also be used for AM and SSB radios. Sensitivity is quoted as a microvolt level that will deliver a 12-dB SINAD. It has been determined that voice can be adequately recovered intelligently with a 12-dB SINAD value. A typical sensitivity rating maybe 0.35 microvolt for a 12-dB SINAD.
Noise in the Microwave Region
Noise is an important consideration at all communication frequencies, but it is particularly critical in the microwave region because noise increases with bandwidth and affects high-frequency signals more than low-frequency signals. The limiting factor in most microwave communication systems, such as satellites, radar, and radio telescope astronomy, is internal nois. In some special microwave receivers, the noise level is reduced by cooling the input stages to the receiver, as mentioned earlier. This technique is called operating with cryogenic conditions, the term cryogenic referring to very cold conditions approaching absolute zero.
Noise in Cascaded Stages
Noise has its greatest effect at the input to a receiver simply because that is the point at which the signal level is lowest. The nois performance of a receiver is invariably determined in the very first stage of the receiver, usually an RF amplifier or mixer. The design of these circuits must ensure the use of very low-noise components, taking into consideration current, resistance, bandwidth, and gain figures in the circuit. Beyond the first and second stages, noise is basically no longer a problem.
The formula used to calculate the overall noise performance of a receiver or of multiple stages of RF amplification, called Friis’ formula, is
where NR = noise ratio
NR1 = noise ratio of input or first amplifier to receive the signal
NR2 = noise ratio of the second amplifier
NR3 = noise ratio of the third amplifier, and so on
A1 = power gain of the first amplifier
A2 = power gain of the second amplifier
A3 = power gain of third amplifier, and so on
Note that the noise ratio is used, rather than the noise figure, and so the gains are given in power ratios rather than in decibels.
power ratios rather than in decibels. As an example, consider the circuit shown in Fig. 9-26. The overall noise ratio for the combination is calculated as follows:
The noise figure is
NF = 10 log NR = 10 log 2.12 = 10(0.326) = 3.26 dB
What this calculation means is that the first stage controls the nois performance for the whole amplifier chain. This is true even though stage 1 has the lowest NR, because, after the first stage, the signal is large enough to overpower the noise. This result is true for almost all receivers and other equipment incorporating multistage amplifiers
ADDITIVE WHITE GAUSSIAN NOISE
Additive white Gaussian noise (AWGN) is a noise term you will hear when discussing the performance of receivers or communications systems in general. AWGN is not a real noise but one that is created for the purpose of testing and comparing receivers and other communications gear. It is most commonly used in digital systems testing were the measure of a system to reproduce a received signal is the bit error rate (BER). BER is the ratio of bit errors that occur to the total number of bits transmitted. For example, if 1,000,000 bits are transmitted and one error occurs, the BER is 1/1,000,000 = 10-6
AWGN is a statistically random noise with a wide frequency range. It is the addition of a flat white or thermal noise to Gaussian noise, which is a nois that is statistically distributed in the form of a Gaussian or standard bell-shaped curve. AWGN is used in modeling or simulating receivers or communications devices like modems with mathematical algorithms in software. The software generates the noise. AWGN can also be generated with hardware in test equipment for testing. Using a standard agreed-upon type of noise allows engineers to determine which receivers, circuits, or equipment produces the best BER.
As you have seen, receiver sensitivity is essentially determined by the noise level encountered in the receiver. The nois is from external sources as well as from receiver components such as transistors and resistors. The RF amplifier in the receiver front-end is the primary contributor to the noise level. For this reason, a low-noise amplifier (LNA) is essential.
The measure of receiver sensitivity can be expressed as signal-to-nois ratio (SNR), noise factor (NF), or SINAD. It can also be expressed as a microvolt level of the input signal. In any case, some criterion must be stated to ensure that the sensitivity is sufficient for the application. For FM radios, the 12-dB SINAD measure is an example. It may also be a specific SNR. In digital radios, bit error rate (BER) is a common measure. Sensitivity is stated in terms of what minimum level of signal will deliver a stated BER. For instance, a receiver sensitivity may have to be at least -94 dBm for a maximum BER of 10-5
One way to calculate sensitivity is to use the expression:
dBm = -174 + 10 log(B) + NF (dB) + SNR (dB)
The -174 dB figure is what we call the noise floor of the receiver. The noise floor is the least amount of noise for a bandwidth of 1 Hz at a room temperature of 290K (17°C) and is calculated with the expression:
P = kTB
the k is Boltzmann’s constant 1.38 x10-23 and T is 290K and B is 1 Hz. P is in watts
P = (1.38 x 10-23)(290)(1) = 4 x 10-21
dBm = 10 log(4 x 10-21/.001) = -174
Now let’s assume that a receiver with a bandwidth of 5 MHz requires an SNR of at least 10 dB to get the desired BER. The receiver nois figure is 6 dB. The minimum receiver sensitivity is:
dBm = -174 + 10 log(B)+ NF (dB) + SNR (dB) = -174 + 10 log (5000000) + 6+ 10 dBm = -174 + 67 + 6 + 10 = -91
A minimum sensitivity of -91 dBm is required.
Remember that the larger the negative number, the better the sensitivity. A sensitivity of -108 dBm is better than a -91 dBm sensitivity. The better the sensitivity, the greater the range between transmitter and receiver can be for a given transmitter output power.
Watch video Noise Level & Types | Conversion Receivers | Signal-to-Noise Ratio (SNR)
Reference : Electronic communication by Louis Frenzel