Signal to noise ratio db Hz. Why is the Internet connection disconnected? Total harmonic distortion

Signal-to-noise ratio (SNR) is the ratio of the rms value of the input signal to the rms value of the noise (excluding harmonic distortion), expressed in decibels:

SNR(dB) = 20 log [ V signal(rms) / V noise(rms) ]

This value allows you to determine the proportion of noise in the measured signal in relation to the useful signal.

The noise measured in the SNR calculation does not include harmonic distortion, but does include quantization noise. For an ADC with a certain resolution, it is the quantization noise that limits the converter's capabilities to the theoretically best signal-to-noise ratio, which is defined as:

SNR(db) = 6.02 N + 1.76,

where N is the resolution of the ADC.

The quantization noise spectrum of ADCs of standard architectures has a uniform frequency distribution. Therefore, the magnitude of this noise cannot be reduced by increasing the conversion time and then averaging the results. Quantization noise can only be reduced by measuring with a larger ADC.

The peculiarity of the sigma-delta ADC is that its quantization noise spectrum is unevenly distributed over frequency - it is shifted towards high frequencies. Therefore, by increasing the measurement time (and, accordingly, the number of samples of the measured signal), accumulating and then averaging the resulting sample (low-pass filter), it is possible to obtain measurement results with higher accuracy. Naturally, the total conversion time will increase.

Other sources of ADC noise include thermal noise, 1/f noise, and reference frequency jitter.

9.2 Total harmonic distortion

Nonlinearity in the results of data conversion leads to harmonic distortion. Such distortions are observed as “spikes” in the frequency spectrum at even and odd harmonics of the measured signal (Fig. 15).

This distortion is defined as total harmonic distortion (THD). They are defined as:

The amount of harmonic distortion decreases at high frequencies to the point where the amplitude of the harmonics becomes less than the noise level. Thus, if we analyze the contribution of harmonic distortion to the conversion results, this can be done either over the entire frequency spectrum, while limiting the amplitude of the harmonics to the noise level, or by limiting the frequency band for analysis. For example, if our system has a low-pass filter, then we are simply not interested in high frequencies and high-frequency harmonics cannot be taken into account.

9.3 Signal-to-noise ratio and distortion

Signal to Noise and Distortion (SiNAD) more fully describes the noise characteristics of an ADC. SiNAD takes into account the magnitude of both noise and harmonic distortion relative to the desired signal. SiNAD is calculated using the following formula:

9.4 Harmonic-free dynamic range

"Specification" ADC

There are general definitions that are commonly used in relation to analog-to-digital converters.

However, the specifications given in the technical documentation of ADC manufacturers can seem quite confusing.

The correct choice of the optimal combination of ADC characteristics for a specific application requires an accurate interpretation of the data given in the technical documentation.

The most commonly confused parameters are resolution and accuracy, although these two characteristics of a real ADC are extremely loosely related to each other. Resolution is not the same as accuracy; a 12-bit ADC may have less precision than an 8-bit ADC. For an ADC, resolution is a measure of how many segments the input range of the analog signal being measured can be divided into (for example, for an 8-bit ADC this is 2 8 = 256 segments). Accuracy characterizes the total deviation of the conversion result from its ideal value for a given input voltage. That is, the resolution characterizes the potential capabilities of the ADC, and the set of accuracy parameters determines the feasibility of such potential capabilities.

The ADC converts the input analog signal into a digital output code. For real converters manufactured in the form of integrated circuits, the conversion process is not ideal: it is influenced by both technological variation in parameters during production and various external noises. Therefore, the digital code at the ADC output is determined with an error. The specification for the ADC indicates the errors provided by the converter itself. They are usually divided into static and dynamic. In this case, it is the final application that determines which ADC characteristics will be considered decisive, the most important in each specific case.

The “specification” of the ADC, given in the technical documentation for the microcircuits, helps to reasonably select a converter for a specific application. As an example, consider the specification of an ADC integrated into the new C8051F064 microcontroller manufactured by Silicon Laboratories.

Before we begin a detailed look at amplifier noise and low-noise circuit design, we need to define a few terms that are often used to describe the noise characteristics of amplifiers. We are talking about quantitative indicators of noise voltages measured at the same point in the circuit. Typically, noise voltages are referenced to the input of the amplifier (although measurements are usually made at the output), that is, the noise of the signal source and the amplifier is described in terms of the equivalent noise voltages at the input that would produce the observed noise at the output. This makes sense when you want to estimate the relative noise added by the amplifier to the noise of the signal source, regardless of gain; This is quite practical, since the main noise of the amplifier is usually generated by the input stage. Unless otherwise stated, noise voltage will always be referenced to the input.

Noise power density and bandwidth.

When considering thermal and shot noise, it was shown that the magnitude of the measured noise voltage depends both on the measurement bandwidth (the wider you look, the more you see) and on the variables (R and I) of the noise source itself. Therefore, it is natural to talk about the root-mean-square noise voltage density:

where is the rms noise voltage measured in a band of width B. At a white noise source, it does not depend on frequency, but pink noise, for example, has a rolloff. The average of the squared noise density is often used. Since it always refers to the root mean square value, and - to the average value of the square, to obtain it, it is enough to square . It sounds simple (and is actually simple), but we want to make sure you don't get confused.

Note that the quantities B and are multipliers for moving from quantities denoted by lowercase letters to quantities denoted by capital letters. For example, for the thermal noise of resistor R we have

The manufacturer's data gives graphs or, respectively, in units of “nanovolt per root hertz” or “volt squared per hertz”. The soon-to-be-introduced quantities are used in exactly the same way.

When adding two uncorrelated signals (two noise or a signal and noise), the squares of the amplitudes are added: , where is the effective (rms) value of the signal obtained by adding the signal with the effective value and the noise with the effective value. Effective values cannot be summed!

Signal to noise ratio.

The signal-to-noise ratio is determined by the formula

where the effective values are indicated for the voltages, and the bandwidth and some central band are specified, i.e. this is the ratio (in decibels) of the effective voltage of the useful signal to the effective voltage of the existing noise. The "signal" can be a sine wave, or a modulated carrier frequency, or even a noise-like signal.

If the signal has a narrow-band spectrum, then it is important in which band the ratio is measured, since it falls if the measurement band becomes wider than the band containing the signal spectrum: as the band expands, the noise energy increases, but the signal energy remains constant.

Noise figure.

Any real signal source or measuring instrument generates noise due to the presence of thermal noise in the internal resistance of the source (the real part of the complex impedance). Of course, there may be additional sources of noise from other causes. The noise figure (NR) of an amplifier is simply the ratio, in decibels, of the output of a real amplifier to the output of a "perfect" (silent) amplifier with the same gain; The input signal in both cases is the thermal noise of the resistor connected to the amplifier input:

where is the mean squared noise voltage per hertz produced by an amplifier with a silent (cold) resistor at the input. The value is significant because the noise voltage generated by the amplifier, as you will soon see, is highly dependent on the source impedance (Figure 7.40).

Rice. 7.40. Dependence of effective noise voltage on noise figure and source resistance. (National Semiconductor Corp.).

Noise figure is a convenient characteristic of the quality of an amplifier if, for a given active source resistance, you want to compare amplifiers (or transistors, for which the noise factor is also determined). The noise figure changes with frequency and source resistance, so it is often given graphically in the form of noise level lines relative to frequency and . It can also be indicated in the form of a set of graphs of its dependence on frequency - one curve for each value of the collector current or a similar set of graphs of the dependence of noise factor on - also one curve for each value of the collector current. Please note the following. The above formula for CN is derived under the assumption that the total input impedance of the amplifier is many times greater than the total impedance of the source, i.e. However, in the special case of RF amplifiers, we usually have Ohms, and the noise factor is defined accordingly. In this special case of matched impedances, it is simply necessary to remove the factor 4 in the previous expressions.

A huge misconception: do not try to improve the situation by adding a series resistor to the signal source to get into the region of minimum noise. All you'll achieve by trying to make an amp look good is add noise to the source! Noise figure can be quite deceiving in this case; It is also deceptive because the noise reduction specification (for example, 2 dB) for a bipolar or field-effect transistor is always given at the optimal combination of and. This value says little about the true performance characteristics, except perhaps that the manufacturer considers it useful to boast of a low CV value.

Generally speaking, when evaluating the characteristics of an amplifier, the easiest way to avoid confusion is to stick to the ratio calculated for a given voltage and source impedance.

Here's how to move from KS to attitude

where is the root-mean-square amplitude of the signal, is the source impedance, and noise factor is the noise figure of the amplifier for a given .

Noise temperature.

Sometimes, instead of noise figure, noise temperature is used to express the noise characteristics of an amplifier. Both methods carry the same information, namely the additional contribution to the noise of the amplifier excited by a signal source with CI impedance; in this sense they are equivalent.

Take a look at fig. 7.41, to understand how noise temperature works: first, imagine that there is a real (noisy) amplifier connected to a noiseless source with impedance (Fig. 7.41, a). If you find it difficult to imagine a silent source, imagine a resistor with a resistance cooled to absolute zero. However, although the source is silent, there will be some noise at the output because the amplifier is noisy. Now imagine the design of Fig. , in which we magically made the amplifier silent and brought the source to some temperature such that the output noise voltage became the same as in Fig. 7.41, a. is called the noise temperature of a given amplifier for source impedance.

As we noted earlier, noise figure and noise temperature are simply different ways of expressing the same information. In fact, it can be shown that they are related to each other by the following relations:

where T is the ambient temperature, usually taken to be 290 K.

Generally speaking, good low noise amplifiers have a noise temperature well below room temperature (or the equivalent of having a noise figure well under 3 dB). Later in this chapter we will explain how you can measure the noise figure (or temperature) of an amplifier. First, however, we need to understand transistor noise and low-noise circuit design techniques. We hope that the following discussions will clarify what is often shrouded in the darkness of misunderstanding.

We're confident that after reading the next two sections, you'll never be fooled by noise figure again!

Notes or textbook covering signal-to-noise ratio, SNR, signal-to-noise ratio measurements, and signal-to-noise ratio formulas.

Noise characteristics and, consequently, signal-to-noise ratio are key parameters for any radio receiver. Signal-to-noise ratio, or SNR as it is often called, is a measure of the sensitivity of a receiver. This is of paramount importance for all applications, from simple radio transmitting devices to those used in cellular or wireless communications, as well as in fixed or mobile radiotelephone communications, two-way radio communications, satellite communications systems and many others.

There are a number of ways in which the noise signature, and therefore the sensitivity, of a radio receiver can be measured. The most obvious method is to compare signal and noise for a known signal level, i.e. signal-to-noise ratio (S/N) or SNR. Obviously, the greater the difference between the signal and the unwanted noise, i.e., the greater the S/N ratio or SNR, the better the sensitivity of the radio receiver.

As with any sensitivity measurement, the performance of the radio receiver as a whole is determined by the performance of the final amplifier stage. Any noise that arrives at the input of the first stage of the RF amplifier will be summed with the signal and amplified in subsequent amplification stages of the receiver. In the case when the noise entering the first stages of the RF amplifier will be amplified to the greatest extent, this AMP will become the most critical, from the point of view of receiver sensitivity, in terms of performance. Thus, the first amplifier of any radio must be low noise.

Concept of signal-to-noise ratio SNR.

Although there are many ways to measure the sensitivity of a radio receiver, C/N ratio or SNR is one of the simplest and is used in a variety of applications. However, it has a number of limitations and although it is widely used, other methods, including noise figure, are also often used. However, the S/N ratio or SNR is an important indicator and a widely used measure of receiver sensitivity.

The difference is usually defined as the signal to noise ratio (S/N) and is usually expressed in decibels. Since the input signal level obviously has an influence on this ratio, the input signal level must be known. It is usually expressed in microvolts. Typically, a certain input signal level is required to achieve a signal-to-noise ratio of 10 dB.

Signal-to-noise ratio formula

Signal-to-noise ratio is the ratio between the desired signal and the unwanted interfering noise.

It is more common to see the signal-to-noise ratio expressed in logarithmic units using decibels:

If all components are expressed in decibels, then the formula can be simplified to:

The power value can be expressed in levels such as dBm (decibel relative to milliwatt or some other value whose levels can be compared).

Effect of Bandwidth on SNR

A number of other factors, in addition to the main indicators, can affect the signal-to-noise ratio, SNR. The first factor is the actual bandwidth of the receiver. Since noise spreads over the entire frequency range, we found that the wider the receiver bandwidth, the higher the noise level. Accordingly, the receiver bandwidth must be determined.

In addition, it was found that the use of amplitude modulation affects the level of modulation. The higher the modulation level, the higher the audio signal at the receiver output. When measuring the noise level, the audio output signal of the receiver is also measured and, accordingly, the level of AM modulation is affected.

Typically a modulation factor corresponding to 30% is selected for this measurement.

Signal to Noise Ratio Specification

This method of measuring efficiency is most often used for RF receivers. Typically, you can expect an S/N ratio figure in the region of 0.5 µV per 10 dB bandwidth of 3 kHz with OBP or Morse. For AM, you can expect an S/N ratio of 1.5 µV at 10 dB and a bandwidth of 6 kHz at a modulation level (AM) of 30%.

What to pay attention to when measuring signal-to-noise ratio

SNR is a very convenient way to quantify receiver sensitivity, but there are some points to consider when interpreting and measuring signal-to-noise ratio. When investigating this, it is necessary to pay attention to the way the signal-to-noise ratio, SNR, is measured. A calibrated RF signal generator is used as a signal source for the receiver. It must have a precise method for adjusting the output level to very low signal levels. Then, at the receiver output, a universal AC voltmeter is used to measure the output signal level. When measuring signal-to-noise ratio, there are two main measurement quantities. One is the noise level and the other is the signal level. As a result of the way the measurements are made, often the measurement of the wanted signal also includes noise, i.e. it is a signal + noise measurement. This is generally not too much of a problem since the signal level is expected to be much higher than the noise level. In this regard, some receiver manufacturers will indicate a slightly different ratio: namely signal and noise to noise (S+N)/N. In practice, the difference is not big, but the ratio (S+W)/W is more correct.

RP and EMF. Sometimes the specification of a signal generator mentions that it is either a voltage difference generator or an EMF generator. This is actually very important because there is a 2:1 ratio between the two levels. For example, 1 µV EMF and 0.5 µV RP are the same. EMF (electromotive force) is the open circuit voltage of the generator, while DP (potential difference) is measured when the generator is loaded. The result of the way the oscillator circuit operates assumes that a real load (50 ohms) is applied. If the load is not equal to this value, an error will occur. Regardless, most equipment will take PP values unless otherwise specified.

Although there are many parameters that are used to indicate the sensitivity characteristics of radio receivers, the signal-to-noise ratio is one of the most basic and easily understood. Therefore, it is widely used for various radio receivers used in applications ranging from radio reception to fixed or mobile radio communications.

Main reasons for low noise performance

The main reasons for high noise levels in signaling systems are:

If the spectrum of the desired signal differs from the spectrum of the noise, the signal-to-noise ratio can be improved by limiting the system bandwidth.

To improve the noise characteristics of complex systems, electromagnetic compatibility methods are used.

Measurement

In audio engineering, the signal-to-noise ratio is determined by measuring the noise voltage and signal at the output of an amplifier or other sound-reproducing device with an rms millivoltmeter or spectrum analyzer. Modern amplifiers and other high-quality audio equipment have a signal-to-noise ratio of about 100-120 dB.

In systems with higher requirements, indirect methods for measuring the signal-to-noise ratio are used, implemented on specialized equipment.

In music

The signal-to-noise ratio is a parameter of an amplifier for active speakers; it shows how much noise the amplifier makes (from 60 to 135.5 dB) if, in the absence of a signal, the volume control is turned to maximum. The higher the signal-to-noise value, the clearer the sound the speakers provide. It is desirable that this parameter be at least 75 dB; for powerful speakers with high-end sound, at least 90 dB.

In the video

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Technical Translator's Guide Signal to noise ratio G/s d - a value characterizing the change in the gradient G against the background of the optical density of an equally exposed radiographic image. Source …

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- signalo ir triukšmo santykis statusas T sritis automatika atitikmenys: engl. signal to noise ratio vok. Signal/Rausch Verhältnis, n rus. signal-to-noise ratio, n pranc. rapport signal/bruit, m … Automatikos terminų žodynas- signal-to-noise ratio The ratio of the peak value of the magnetic transducer signal, caused by a change in the measured characteristic of the magnetic field, to the root mean square value of the noise amplitude caused by the influence of interfering parameters... ... - - [Ya.N.Luginsky, M.S.Fezi Zhilinskaya, Yu.S.Kabirov. English-Russian dictionary of electrical engineering and power engineering, Moscow, 1999] Topics of electrical engineering, basic concepts EN signal to noise ratioS/N ratio ...

integrated circuit signal-to-noise ratio- signal-to-noise ratio The ratio of the effective value of the output voltage of an integrated circuit containing only low-frequency components corresponding to the frequencies of the modulating voltage to the effective value of the output voltage at ... - - [Ya.N.Luginsky, M.S.Fezi Zhilinskaya, Yu.S.Kabirov. English-Russian dictionary of electrical engineering and power engineering, Moscow, 1999] Topics of electrical engineering, basic concepts EN signal to noise ratioS/N ratio ...

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