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发表于 2009-7-17 23:26:51
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For a non-linear system, if one injects a pure signal with frequency - w1, the output contains the frequencies of w1, 2*w1, 3*w1, ..., n*w1, ..... the n*w1 is called the n order harmonic. Usually, the 2*w1, 3*w1, .. , n*w1,.. are far away from the desired frequency - w1 and could be easily filtered out. For example, w1 = 2.5 GHz, the 2*w1 is 5 GHz, it could be filtered out easily by a low pass filter or band pass filter. Even without a filter, the attenuation of the following circuits for the 5 GHz signal or higher frequency signal could be high because of the parasitic capacitance of the IC. If the system operation band (BW) is at w1, the 2*w1 component itself in the output is also small. For the higher order harmonics, the situation is the same. It seems that the harmonic could not be a big trouble. But it needs to be satifisfied some requirements, such as the FCC limitation. For the transmitter, the n order harmonic could not be high enough to disturb other devices in working, e.g. there is another IC working in 5 GHz.
However, the bad thing could happen if several signals with closed different frequencies are injected to the non-linear systems. We will discuss it later why it is not good. First, one may ask could it often happen in the wireless communication system for the signals with different frequencies injecting at the same time. Unfortunately, it always happen in the modern communation system. Thinking about one simple wireless communication system: the positive half cosine stands for the symbol "1" and negative half cosine stands for the symbol "0". This system output random series data: 010001110101010.... In the frequency domain, the spectrum likes a symmetric 'mountain' shape inside the band (you can do the simulation by Matlab or theoriticall derivation to figure out why it is like the 'mountain' shape). That means the signal contains any frequencies in the band. Now, we can discuss why it is not good for the closed different frequencies injecting into the non-linear systems. For simplicity, let's take a look at two signals with w1, w2 of frequencies. Notice that the w1 and w2 are close enough. For example w1 = 2.5 GHz, and w2 = 2.5 GHz + 100 kHz. The seperation between w2 and w1 is deltaw=w2-w1 = 100 kHz. Assuming the operation bandwidth is 3 MHz, from 2.5 GHz - 1.5 MHz to 2.5 GHz + 1.5 MHz. These two signals will form the frequencies after the non-linear system: w1, w2, 2*w1, 2*w2, w1+/- w2, 3*w1, 3*w2, 2*W1-W2, and 2*W2-W1. The frequency w1, w2 are the desired frequencies. 2*w1, 2*w2, w1+/-w2, 3*w1, and 3*w2 are all far away from the operation band (2.5GHz-1.5 MHz ~ 2.5 GHz + 1.5 MHz). For example, w2-w1 = 100 kHz (far away from 2.5 GHz). The 'bad' items are the 2*W1 -W2 = 2.5 GHz - 100 kHz, and the 2*w2-w1 = 2.5 GHz + 200 KHz. Those two items fall into the operation band and will cause interferences (can be seen as noise). The item - w1+/-w2 is called 2-order inter-modulation (IM2) and 2*w1-w2, 2*w2-w1 are called the 3-order inter-modulation (IM3). The w1 or w2 desired signals are call the fundamental signals.
Because the IM3s is the most concerned items, we need to give a definition to reflect the system IM3 performance. First we input two equal amplitude signals for w1 and w2 and draw the output fundamental (at w1 or w2, because they are really close, the output should be nearly the same) and IM3 (at 2*w1-w2, or 2*w2-w1, their amplitudes are also close) versus input power in the plot. The x-axis and y-axis is in log scale. At the low input power level, the fundamental plot is a straight line with 1db/db of slope and IM3 is also a straight line with 3db/db of slope. The IM3 is much smaller than the fundamental but grows faster than the fundamental with the increasing input power. If we make the extrapolation lines for both of the fundamental and IM3 in the plot, the two extrapolation lines will meet at one point. That point means the undesired extroplated IM3 has the same amplitude as the desired fundamental signal. After that point. the extropalated IM3 is higher than the desired signal. In another word, the desired signal is 'submerged' by the 'noise'- IM3 after that point. The input power corresponding to that point is called the 3 order inter-modulation input power (IIP3) and the output power at that point is called the 3 order inter-modulation output power (OIP3). It is worthy to notice that the point is only a extropalated/supposed point. In the real system, the output power and IM3 will be saturated with the high input power before that point. That may make the IM3 plot never meet the fundamental plot. That is why the point is only a extropalated point for most of the system. To define the fundamental saturation situation, there is another definition -- -1 dB compression point (-1dB CP).
To summary, the IIP3 is a performance, which specifies the 3rd non-linearity of a circuit/block/system. In details, it is the input power corresponding to the point, at which the extropolated output IM3 is equal to the extropolated fundamental signals. The IIP3 is about 2-tone signals - w1 and w2, and the IM3 also has two items: the 2*w1-w2 is called left IM3 (it locates at the left side of w1) and 2*w2-w1 is called right IM3 (it locates at the the right side of w2). There are four items are close to each other (the separations are the same: deltw=w2-w1), the left IM3 and right IM3 are undesired (noise!). They will disturb the circuit itself, because they are all falling into the band (or channel) in our case. The IIP3 in this case is called close IIP3. One can image another case: the IM3 is out of the band. If the seperation between w1 and w2 is large enough to let the IM3 out of the band, e.g. w1 = 2.5 G - 1MHz and w2 = 2.5 G + 1MHz, delta w = 2MHz. The left IM3 is 2.5 G - 3MHz, it is out of the operation band (2.5 GHz - 1.5 MHz ~ 2.5 GHz + 1.5 MHz) and fall into the neighbour channel. The IIP3 in this case is called far IIP3. Usually, the communation system has multiple channels. Assume the 2.5G -1.5 MHz ~ 2.5 GHz + 1MHz is one channel (the operation channel) and 2.5 GHz - 4.5 MHz ~ 2.5 GHz - 1.5 GHz is another channel (may in use by another block at the same time). Compared to the disturbance of close IIP3 on the operation channel, the far IIP3 has effects on the other channel operation of the system or others.
[ 本帖最后由 workerabc 于 2009-7-17 23:30 编辑 ] |
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