RF

 

 

 

Dynamic Range

 

Dynamic Range is a very wide and a little bit ambiguous term. It may vary with the context and the system you are referring to. (NOTE : you may get various professional definition of Dynamic Range in reference section. This note is very casual definition mostly based on my own experience and understanding).

Let's build the idea up in three steps. First we separate dynamic range from input power range, because a datasheet usually gives only the second one. Then we look at how equipment moves a fixed dynamic range along the power axis. Finally we put numbers on the two edges of the range: the noise floor at the bottom and distortion at the top.

What is dynamic range, and how is it different from input power range ?

Two numbers on a datasheet are both loosely called a range, and they answer different questions. One number says what a system can handle at one moment. The other says what it can handle over time, after you change its settings. Let's pin down the first one before we compare them.

My definition of Dynamic Range is 'a range of input power to a certain system (or component) in which the weakest and strongest signal can be detected simultaneously without change of any input configuration. The keywords in this definition is 'simultaneously' and 'without changing any input configuration'. It seems that this term is often confused with the term 'input power range'.

Input Power Range usually refers to the range of the power in which the sytem can detect the power which is not necessarily simultaneously and input configuration change is also allowed. In most case, if you look into a datasheet of an equipment the input range is printed much wider than the dymaic range. Usually equipment vendor would not put the dynamic range information in the datasheet, but in the operation of the system there are many cases where the dynamic range is more important than the input power range.

For example, let's think of following situation. In this case, it is assumed that Dynamic Range of a system is set to be as in shaded area. As you would notice obviously, the signal (A) and (B) can be properly detected since they are all within the dynamic range and (C) would fail to be detected since the power is too high and (D) would also fail to be detected since the power is too low.

 

Power versus time plot with a shaded Dynamic Range band, signals A and B inside it, signal C above it and signal D below it

One fixed setting, four signals. Only the signals whose power stays inside the shaded band are detected.

  • The vertical axis is Power and the horizontal axis is Time. The shaded band between the two arrow marks on the right is labelled Dynamic Range.
  • Signal (A) swings near the top of the band and signal (B) near its bottom. Both are drawn in the same time span, so the system detects them together.
  • Signal (C) comes later and sits above the band. Its peaks go past the top edge, so the system overloads.
  • Signal (D) comes last and sits mostly below the band. Most of its swing falls under the bottom edge, so the system cannot separate it from its own noise.

Notice that (A) and (B) arrive at the same time. That is the word 'simultaneously' in the definition. The system must see the strong one and the weak one in the same measurement, with the same gain and the same attenuation. This case is common in practice. For example, a UE receiver sees a weak wanted signal and a strong signal in the adjacent channel at the same moment. A spectrum analyzer shows a carrier and its small spurious emissions in the same sweep.

  • Dynamic range is measured at one fixed setting : it is the gap between the strongest and the weakest signal that the system handles at the same time.
  • Input power range allows a change of setting : it covers signals that arrive at different times, with the input configuration changed in between.
  • A signal above the range overloads the system : a signal below the range is lost in the noise of the system.

Why is the input range of equipment wider than its dynamic range ?

The datasheet number and the working number differ for a practical reason. Most equipment cannot make its dynamic range wider. But it can move that range up or down the power axis, and the total span it can move over is the input range.

In some system (actually in most of the system (e.g, wireless communication call box) if it is not a single component, the system would be designed in such a way that you can shift the input level at different moment of measurement by manually or automatically. In this case, dynamic range itself does not change, but the position in power axis of the dynamic range can change. Due to this kind of design, those equipment states its Input range to be much wider than the dynamic range of the input chain. If you know of the rough power range of your input signal, you may configure your system to work in much more wider range than the dynamic range.

The plot below takes the same four signals and splits the time axis into three periods. In each period the shaded band has the same height, but the system has moved it to a different power level.

 

Power versus time plot split into periods I, II and III, with the shaded band moved to cover A and B, then C, then D, and an Input Range arrow spanning all three positions

The band keeps its height and changes its position. The Input Range is the span of all positions, not the height of one band.

  • In period (I) the band sits where it was in the plot above. Signals (A) and (B) are inside it.
  • In period (II) the band has moved up to cover signal (C).
  • In period (III) the band has moved down to cover signal (D).
  • The arrow on the right, labelled Input Range, runs from above the highest band to below the lowest band. It is much taller than any single band.

This is how a signal analyzer or a call box works. You set a reference level or an expected input power, and the instrument chooses its input attenuation and gain for that level. A UE receiver does the same thing with its AGC. The move takes time, and it must happen before the signal arrives. So the wide input range helps only when the signals come one after another. If (A) and (C) arrive at the same time, no single position of the band covers both. In that case the dynamic range is the number that decides the result.

  • The input range is the span over which the band can move : the band itself keeps the height of the dynamic range.
  • The setting must be chosen before the signal arrives : this is why test equipment asks for an expected power or a reference level.
  • Simultaneous signals need the dynamic range : a wide input range cannot help when a strong and a weak signal arrive together.

What sets the bottom and the top of the dynamic range ?

So far the dynamic range has been a shaded band with no numbers on it. Let's put numbers on its two edges. Each edge comes from a different physical effect, so each one is improved in a different way.

The bottom edge is the noise floor. Every resistor produces thermal noise, and at the reference temperature of 290 K its power density is kT, about -174 dBm/Hz. The receiver adds its own noise on top, and the noise figure NF measures that addition. So the noise floor in a bandwidth B is -174 dBm/Hz + 10log10(B) + NF. For example, a receiver with B = 1 MHz and NF = 10 dB has a noise floor of -174 + 60 + 10 = -104 dBm. A signal weaker than this is hidden in the noise. A narrower bandwidth lowers the floor by 10 dB for every factor of ten. That is why a spectrum analyzer shows a lower noise floor with a smaller RBW.

The top edge is distortion. A strong signal pushes the amplifier and the mixer into their nonlinear region. The first sign is gain compression, and the input level where the gain has dropped by 1 dB is P1dB. Before that point, a second problem appears when two strong signals are present at the same time. They mix and create third order intermodulation products at 2f1 - f2 and 2f2 - f1. These products fall close to the wanted signals, so a filter cannot remove them. Their power rises 3 dB for every 1 dB of input power. The input level where the extrapolated products would equal the wanted signals is IIP3. Referred to the input, each product has a power of 3Pin - 2IIP3, with all values in dBm.

Now we can combine the two edges into one number. The spurious free dynamic range SFDR is the range of input power in which the intermodulation products stay below the noise floor. It is 2/3 x (IIP3 - noise floor). Let's continue the example with IIP3 = +10 dBm. The SFDR is 2/3 x (10 + 104) = 76 dB. At its upper limit each input tone is -28 dBm, and each product is 3 x (-28) - 2 x 10 = -104 dBm, exactly at the noise floor. SFDR is measured with two signals present at the same time. So it is the closest standard number to the definition at the top of this page.

Other definitions give other numbers for the same receiver. For a pure third order nonlinearity, P1dB at the input is about 9.6 dB below IIP3, so it is about +0.4 dBm here. The range from the noise floor to P1dB is then about 104 dB, which is much wider than the SFDR. This is one reason why dynamic range is an ambiguous term. Before you compare two datasheets, check which top edge and which bandwidth each one uses.

A digital receiver adds one more limit, the ADC. An ideal N bit ADC gives a signal to quantization noise ratio of 6.02N + 1.76 dB for a full scale sine wave, measured over the whole Nyquist band. A 12 bit ADC therefore gives about 74 dB, and a 14 bit ADC about 86 dB. The AGC in front of the ADC moves the signal inside this range. It is the same idea as the moving band in the plot above.

  • The bottom edge is the noise floor : -174 dBm/Hz + 10log10(B) + NF, so both a narrower bandwidth and a lower NF extend the range downward.
  • The top edge is distortion : gain compression for one strong signal, and third order intermodulation for two strong signals.
  • SFDR is 2/3 x (IIP3 - noise floor) : with a -104 dBm noise floor and IIP3 = +10 dBm, it is 76 dB.
  • Always check the definition behind a number : the same receiver has about 104 dB up to P1dB, but only 76 dB of SFDR.

Reference