Noise

Definition:

Unwanted signals. Noise comes from both external sources -- such as the AC power line, motors, generators, transformers, fluorescent lights, soldering irons, CRT displays, computers, electrical storms, welders, and radio transmitters -- and internal sources, such as digital clocks, microprocessors, and switched mode power supplies. Video system noise can take various forms, including snow, which is a random video noise.

Noise may either be transient in nature, have fixed frequencies such as harmonic or mixer products, or be broadband random noise.

Noise and the Fundamental Noise Equations:
Noise, and its effect on electronic communication, is defined in many ways. At times, these definitions become so convoluted that they, in turn, contribute to the “noise” of the subject. For example, there are (sometime conflicting) definitions of white noise, pink noise, thermal noise, shot noise, equivalent noise, signal-to-noise, noise factor, and noise figure. In addition, there are such titillating subjects as antenna noise, partition noise, flicker noise, ground loops, and noise power density.

For the purposes of this document, we will limit our investigation of noise to the following illustrations and equations. First, assume the circuit as shown in Figure 3. This schematic resembles a simplified representation of a base-band laboratory signal generator where the Sig is assumed to be the signal output, which is noise free. However, the generator also has a noise output, and it is represented by R_noise, the generator’s internal resistance. This figure assumes that R_Noise and R_Load are matched, and thus, have the same value.

Figure 3 The elementary thermal (resistive)Noise Generator. The (Thevenin) resistor RNoise is assumed to be the only noise source -- the (Thevenin) Signal Generator and RLoad are considered noise free.

The noisepower produced by a given, defined resistor noise source is approximately:

Where:
PN = The thermal noise power output of a resistor
k = Boltzmann’s constant = 1.38*10-23 joules/K
T = absolute temperature, K = 273 + C
f = the system’s bandwidth

For example, assume T = 27C = 300k, f = 60MHz - 50MHz = 10MHz. Then:

The noisevoltage produced by RNoise is approximately:

Note: The word "approximately" was used because both the noise power and the attendant noise voltage are statistical -- these are random values.

For example, assume T = 27C = 300k, f = 60MHz - 50MHz = 10mhz, R = 10k. Then:

Next, the ideas and equations just presented can be expanded to include an amplifier as shown in Figure 4.

Figure 4 The rudiments developed in Figure 3 are expanded to included a amplifier with a gain of A. Here the term “amplifier” can mean, for instance, the input stage to a radio, TV, or a radar, or it can also be construed to be the entire RF and IF stages of these systems.

Using Figure 4, the amplifier’s signal input (across R_In) voltage and power are:

Likewise, using Figure 4, at the amplifier’s input:

Figure 5 The schematic of an amplifier system based on the idea of an Equivalent Noise Resistance or Rn. [1] shows the rudimentary idea of an input with Vsignal, Rsignal, and Rin. [2] shows only the input circuit with Vsignal and Rthev, where R_thev is the Thevenin equivalent of Signal and R_in. In both [1] and [2], The X boxes show the inputs to a “perfect” (noise free) amplifier with a gain of A.

After deriving the above equations relating to the signal at the amplifier’s input, you can derive the (equivalent) signals at the amplifier’s output. At first blush, it would seem logical to simply multiply the appropriate equations by “A” ( or A2), the amplifiers gain, to produce output values for the appropriate voltages or powers. However, there may be a problem: the amplifier itself may add noise. In an effort to be more accurate and, incidentally, simplify the calculations (more about this later), manufacturers often solve the amplifier noise problem by supplying the user with an item in their data sheet termed Rn.

Rn is a fictitious (equivalent)resistor that “fits” in the following schematic and equations, and gives more realistic output values. Rn represents the amplifier’s total equivalent noise. Although there are many variations on this schematic and its use, the following text and equations show the general idea. The starting point includes these parameters: the value of VSignal; the value of (the now, noiseless) Rsignal; the value of the manufacture’s Rn; and the gain A of the amplifier.

Since there is a voltage division of Vsignal by the parallel combination of R_signal and R_in, they can be combined into a new Thevenin equivalent resistor, R_thev.

The equivalent signal at the (X boxes) terminals is:

The total RMS noise voltage from R_N at the (X boxes) terminals is:

Likewise, the signal-to-noise power is:

For example, using the techniques dependent on R_N, assume: the manufacturer’s R_N is given as 400 ohms, R_S = 50, R_In = 500 ohms, thus R_Thev = 45.45 ohms, the room temperature = 17C = 290K, B = 10 kHz, and ES = 1 V.

Noise -- Time out for a Reality Check

Equations are fine, but what do they mean? Figure 6 shows a very simplified input-system schematic that might resemble that of a radio, TV, or radar. For a starting reference, it is often overlooked that “space,” be it the far outer space or the near space surrounding the earth, has a characteristic impdance (resistance). Although its true value depends on many factors, some (not all) theoretical calculations set it in the order of 200 to 400 ohms. Therefore, to match this space impedance, for maximum power transfer, antennas are usually designed to approximate these resistance values. Again, the exact radiation impedance (or receiving impedance) of an antenna will vary with bandwidth, temperature, and sometimes “Q” if it has reactive components, and so on.

Figure 6 A simplified schematic showing the major components of the input circuit an a radio-type receiver. Each of these components has an associated (often, mostly resistive) characteristic impedance, and thus, an equivalent noise resistance can be derived.

If the antenna is (usually) coupled to the input RF amplifier with a network or an RF transformer, fundamental circuit analysis can show its impedance over any stated bandwidth. Likewise, the amplifier’s input impedance -- it may be reactive in addition to its input resistance -- is often given or can be calculated.

The noise performance for these input elements can also be specified. First, although the noise of space is highly variable, depending on both man-made and galactic factors (for some systems, sun spots are often one variable), theory and experience have coupled to give useful approximations. References on astronomy and cosmology give orders of magnitude for the noise of space under various conditions. The inherent noise of an antenna can be approximated assuming a given resistance and bandwidth using equations [E 1] and [E 2]. The equivalent resistance of any coupling, reactive, or tuned circuit(s) can be calculated by using the “R” value derived from the circuit’s “Q.”

For an amplifier, be it single-stage or multi-stage, the two major noise specifiers are the signal-to-noise ratio (S/N) and thenoise figure. The signal-to-noise ratio is given in [E 11] and [E 12]: since a “perfect” amplifier is assumed, the signal-to-noise is the same at the amplifier’s output as its input. However, if the noise calculations for a given amplifier (or system) do NOT include the fictitious, but very convenient Rn, the output S/N will be different than the previously assumed input S/N. For this latter case, referring back to Figure 4, one set of noise calculations can include:

Likewise, using the ideas depicted in Figure 4, it is common to calculate the amplifier’s noise figure. One form of the equation for the amplifier’s noise figure is:

Yes, these equations work, but, as you may have observed, what is the value of PNoiseOut? The problem is that this can NOT be conveniently calculated: it must be measured with special equipment and that would require another detailed explanation. However, further explanation of PNoiseOut is beyond the scope of this document. Notwithstanding, it was deemed necessary to go this far to show some of the difficulties and hazards in noise calculations and measurements.

Units

V or dB

Information Contributed By:

Bob Libbey, Retired RCA Engineer and Adjunct Professor, New Jersey Institute of Technology

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