TIAs with Matched Filters
From other sections of this website, it is clear that for optimum performance, the TIA should function as a matched filter and the output pulse shape should be a triangular output pulse. In the past, this was not practical at high speeds. Receivers Unlimited has developed a simple method of implementing matched filters in a practical way.
The following eye diagram shows a circuit simulation results from a Spice transient analysis of a time dependent TIA circuit set up to create a matched filter.
Comparison of Typical RC filter vs Matched Filter TIA
In this section, we take a "typical" transimpedance amplifier design and compare with a stationary matched filter TIA. We choose a stationary matched filter TIA for ease of calculation, the actual Receivers Unlimited designs have a NON stationary TIA which improves results significantly above a stationary TIA.
If we look at the transfer function (S21) of both TIAs in the frequency domain, it is easier to see the noise advantages. The standard TIA design has a single pole RC filter shape and a 3dB BW of about 70% of the bitrate (ie for a 10GE receiver, the BW of the photodetector + TIA + package would be about 7GHZ.) The matched filter design is quite different, in fact, the 3dB BW is no longer a good metric for the noise performance because the shape of the frequency response curve is so different. The roll off of the transfer function from DC is much steeper and the 3dB point is at a much lower frequency. In fact, for a matched filter, the frequency response curve (S21) is an image of the Fourier transform of the input data! In other words, the transfer function of the matched filter MATCHES the power spectrum of the incoming data.
The transfer function plot below shows a typical TIA with a RC filter response and a TIA with a matched filter response. The red curve is the RC TIA with a 3dB bandwidth(BW) of .7 x Bit Rate and the blue curve is the matched filter response. One can easily determine the matched filter 3dB BW is LESS than 50% of the bitrate and a careful calculation shows the 3dB BW to be about 44% of the bitrate. Obviously, this lower BW improves the noise performance over the RC filter case. In addition, it can be seen that the filter response falls very rapidly and reaches zero at the bitrate and each harmonic of the bit rate. These nulls fall exactly where the power spectrum of the data also has a null; the filter is designed not to bring in noise energy where there is no data energy. This matching of the nulls helps demonstrate why this shape is optimum for improving the SNR.
S21 for RC TIA(red) and Matched Filter TIA(blue)
At the output of the TIA, all of the extra gain in the area above the matched filter blue curve and below the RC filter red curve is additional noise that is passed by the RC filter but eliminated by the matched filter. All of the extra noise simply corrupts the original signal.
As the plot shows, the RC filter brings in many dB of extra noise, compared to the matched filter.
The above plot makes it obvious why stationary matched filters are used in most communication systems. Most communication texts cover the stationary case and show a 1-2dB improvement, however by using time varying techniques the theoretical improvement is greater than 3dB.
In the past, a matched filter was not practical to implement at the highest speeds. Now, Receivers Unlimited has practical TIA designs that start with matched filter performance and improve upon that base.
Does anyone use Matched Filters Today?
The technology of matched filters is
very common in DSPs and lower speed digital communications. See the
links page for more info on matched filters in communications. Today,
however, matched filter technology is not common in high speed optical communications.
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