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The sensitivity is as follows. This equation defines the signal power in dB Watts that is present at the demodulator for a desired carrier to noise ratio. Let s explain each of the terms in this equation. The total thermal noise power kTB is a function of three quantities, 1 Boltzmann s constant k in Joules K, 2 temperature in Kelvin, and 3 the overall bandwidth of the channel selective filtering in the receiver.
Thermal Noise floor k Joules K T K B Hz. The resulting noise is in Joules Second or Watts. This is referred to as Thermal Noise because of the dependency on temperature. To convert the noise power to dB Watts, use 10 times the log of the noise power in watts. If we look at the normalized B 1 Hz bandwidth noise floor equation, we have.
Next, to convert from dBWatts to dBmilliwatts dBm increase this value by 30 dB. 9 dBW Hz 30 dB -173. This is the amount of noise power in a 1 Hz bandwidth. Figure 1 Noise power in a 1 Hz bandwidth. What is Noise Figure. The Noise figure is the amount of noise power added by the electronic circuitry in the receiver to the thermal noise power from the input of the receiver. The thermal noise at the input to the receiver passes through to the demodulator. This noise is present in the receive channel and cannot be removed.
The noise figure of circuits in the receiver such as amplifiers and mixers, adds additional noise to the receive channel. This raises the noise floor at the demodulator. What is Carrier to Noise Ratio C N. In order to achieve the desired quality of demodulated signal, the signal power must be higher than the noise floor. The required ratio of signal power to noise floor is known for certain types of modulation. For an analog FM land mobile radio system using 25 kHz channels, the receiver must have approximately 4 dB more signal power than noise power.
This represents a carrier to noise ratio 4 dB. Figure 2 Noise Figure added to thermal noise kTB. Bit Error Rate BER is the sensitivity benchmark for digital modulation systems. Eb No is the ratio of the Energy per bit Eb to the noise spectral density No - the noise power present in 1 Hz. The carrier to noise ratio required for a certain BER is a function of the Eb No of the signal. This is a digital system representation of signal to noise ratio.
Each digital modulation type has a Eb No curve Eb No vs. In order to determine sensitivity, use the appropriate curve and find desired bit error rate to determine the necessary Eb No. Where Fb is the bit rate and B is the receiver equivalent noise bandwidth. Then calculate the Carrier to noise ratio by the following relationship.
Figure 3 Carrier to Noise ratio. What is Equivalent Noise Bandwidth. A filter s equivalent noise bandwidth ENBW is defined as the bandwidth of a perfect rectangular filter that passes the same amount of power as the cumulative bandwidth of the channel selective filters in the receiver. Figure 4 Noise Power in the IF Bandwidth. At this point we would like to know the noise floor in our receiver, i.
the noise power in the receiver intermediate frequency IF filter bandwidth that comes from kTB. Since the units of kTB are Watts Hz, calculate the noise floor in the channel bandwidth by multiplying the noise power in a 1 Hz bandwidth by the overall equivalent noise bandwidth in Hz. For a receiver with a 10 kHz ENBW, we calculate the noise floor in dB milliwatts dBm as follows. 38 10-23 290 1 Hz 10000 30 134.
Next we see how the bandwidth of a perfect rectangular filter compares to the actual filter response of the channel selective filters in the receiver. Figure 5 Perfect filter that passes same power. We use the bandwidth of the equivalent ideal rectangular filter ENBW to calculate the thermal noise floor. We may specify the equivalent noise bandwidth for design purposes but in practice, it is the composite bandwidth of all of the filters in front of the demodulator. The power that a filter can pass is a function of the area under the filter curve.
The filter plot is in dB. Figure 6 Area under filter response. Calculating ENBW from Measured Data. Ideally, we calculate the 2-sided ENBW by integrating the normalized filter power frequency response curve from -infinity to infinity fs 2 to fs 2 for a digital filter sampled at a rate of fs. For practical purposes the -60 dB BW values of the normalized filter response can be iq option 6.3.2 apk as the limits of integration. The integration must be done in linear terms of watts or milliwatts not dB.
Scattering parameters or S-parameters are a measurement of how radio frequency RF voltage propagates through an RF network. Since we are looking for bandwidth in Hertz, we do not need to know the absolute power under the curve. S-parameters of an RF filter can easily be measured using a network analyzer. Since S-parameters are voltage related measurements, we can convert them to a power quantity by the relationship.
Figure 7 Integration by summation of rectangles. We can use the magnitude of the through response S21 as the voltage term and normalize the impedance to 1 Ohm to substitute into the Power equation. This will give us a linear power term. For our case we choose S parameters where the magnitude is in dB. The power must be converted to a linear term for our calculations. We then calculate the bandwidth using the measured S-parameter data. For the overall ENBW, we want a rectangle where the height of the rectangle is equal to the maximum power S21 2.
The area of the rectangular filter is equal to the area under the filter curve. Calculate the area of the under the IF filter response curve by using numerical integration by uniform rectangles. Find the area of each uniform rectangle by multiplying S21 2 power by the frequency step size used in the S parameter data. For a simple rectangle. Therefore, the ENBW is.
Since the S21 terms are unitless we now have a result that is frequency in Hertz. The result is the bandwidth of a rectangular filter with infinite stopband rejection that passes the same amount of power as the filter that we measured S parameters. It is this bandwidth that we will use in our calculation of the receiver noise floor kTB. We may use software to calculate a filter s ENBW.
Here is a Matlab script for calculating ENBW from an. s2p s-parameter data file. Figure 8 Matlab code to calculate ENBW of a filter using s parameters. Sometimes a digital filter implemented as a lowpass filter in DSP is the narrowest filter in a given system. Here is a Matlab script that will calculate the ENBW of a digital lowpass filter given a text file that contains the taps for the filter.
Figure 9 Matlab code to calculate ENBW of a filter using FIR filter taps. Now We Can Calculate Receiver Sensitivity. We have quantities for each of the elements of the equation for receiver sensitivity. To calculate receiver sensitivity, we add the overall noise figure of the receiver to the noise floor. This quantifies the noise floor at the input to the demodulator. The signal must be higher than the noise floor by the carrier to noise ratio required for a desired signal quality.
When these things are added, the result is the power level required to meet the figure of merit for usable information referred to as Reference Sensitivity. We can calculate the sensitivity of a receiver with a 5 dB noise figure NF for analog FM in a 25 kHz channel, using the noise floor in a 10 kHz ENBW receiver that we calculated earlier. The carrier to noise ratio required for 12 dB SINAD in an analog FM receiver with a 10 kHz ENBW is approximately 4 dB. Substitute the values into. Equation 10 as follows.
Sensitivity 10 log10 kT 10000 30 dB 5 dB 4 dB. 0 dBm 5 dB 4 dB. Figure 10 Thermal Noise kTB plus NF plus C N. The sensitivity of a receiver is a function of band limited thermal noise, receiver noise figure, and the required carrier to noise ratio for a particular modulation. The equivalent noise bandwidth refers to the amount that the noise is band limited. Iq option 6.3.2 apk often contain narrow bandpass hardware filters as well as narrow lowpass filters implemented in digital signal processing DSP.
Using these characteristics, we can accurately calculate sensitivity of a receiver. It is possible to estimate the ENBW, but it can be calculated from measured data or DSP filter taps. Dennis Layne is a Senior Principal RF Engineer at Harris Corporation. Dennis has a Bachelor s of Science in Physics from Lynchburg College in Virginia and has 18 years experience designing receivers for Land Mobile Radio. The August 2020 Online Edition is now available for viewing and download.
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Even though we do not suggest using only one indicator, if one had to, the 2-period RSI would be the indicator. By Galen Woods in Trading Setups on February 21, 2014. Larry Connors is an experienced trader and publisher of trading research. Together with Linda Raschke, he wrote the book, Street Smarts, which is a solid collection of trading strategies including the Holy Grail. Trading Rules 2-Period RSI Strategy. What is so fantastic about the 2-period Relative Strength Index RSI that a well-regarded trader like Larry Connors would suggest it as the one indicator.
Coupling an oscillator with a trend indicator is the usual approach. For instance, Connors recommended the 200-period moving average, and StockChart. com did just that in their RSI2 examples. Let s do away with a separate trend indicator, and let the 2-period RSI clue us in on the trend. I always enjoy putting less on my charts. The 2-period RSI like the 2-period ADX is extremely sensitive. However, I added a twist to this fast oscillator.
Of course, most of these overbought signals will fail because the 2-period RSI is not meant for locating significant reversals. How I Trade With Only The 2-Period RSI. We expect the 2-period RSI will give many overbought signals during an uptrend.
Coments:19.03.2020 : 05:27 Tegami:
Leading indicators are an important, helpful, and easy-to-interpret tool of market analysis. Leading Indicators Summary.
22.03.2020 : 20:42 Votaur:
The enable output EN is the first output and it is on when the timer is energized.
20.03.2020 : 13:41 Tut:
3 Attempting to link, load or execute 64-bit non-LDT ABI objects on AIX 5.