Feed Forward Equalizer

A second figure of merit to evaluate a link’s performance is the Bit Error Ratio (BER), which is specified for a given SerDes and used transmission channel, and describes the number of bit errors divided by the total number of bits transmitted. To give an estimation about the expected BER, the signal quality needs to be evaluated, which can be expressed e. g. with an eye diagram, where the signal is repetitively laid several times on top of each other within one UI. A second diagram to express the link’s performance is the bathtub curve, which gives the BER as function of the horizontal sampling position. Depending on the signal quality, there is a larger or smaller space in the center between two crossing points, where no transition has passed, called the eye. The larger that eye, the better the signal quality, since it can be clearly distinguished between two values. The size of the eye is negatively affected in horizontal orientation by high jitter, and vertically by a low signal-to-noise ratio. While voltage noise can lead to sampling errors when the signal vertically passes the logic threshold, jitter may lead to a horizontal shift and a signal transition across the sampling point. The sources of noise and jitter are in part deterministic and random, and can be combined by convolution to the Probability Density Function (PDF), which gives the probability that a transition varies around its expected position by a certain value. Hence, the final BER calculation underlies statistical processes.

On transmitter side, the following deterministic phenomena have an impact on the signal quality, because they all contribute to total jitter:

• Noise

Variations or noise on the clock signal, ground or power supply are directly modulated to the output signal, called sinusoidal jitter, because of its form.

6.2 Architecture

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

ns

Transmitted Waveform Channel Response

Figure 6.5: Channel response of a ideal transmitted waveform. The low-pass

characteristics of the transmission channel will lead to ISI.

Since noise is a physical phenomena, it can only be reduced by layout techniques or environmental conditions.

• Crosstalk

If high-speed data are sent on multiple adjacent lanes a transition coupling can lead to amplitude distortion, resulting in data dependent or random jitter at a very low statistical weight but with a high standard deviation [61]. Crosstalk can also be reduced by careful layout design and spatial considerations.

• Duty-Cycle Distortion (DCD)

DCD can happen on the data as well as on the clock signal. On one hand induced by a reference clock which has a duty-cycle not equal to 50 %, on the other hand by changing switching characteristics of digital logic over PVT corners. Therefore a special duty-cycle correction circuit is used. • Inter-Symbol Interference (ISI)

Since data rates increase and transients have very short rise times, the low pass characteristics of the transmission channel came more and more into play, resulting in noticeable inter-symbol interference. The channel attenuation will blur the signal, which then interferes with subsequent symbols. The phenomena of pulse spreading is depicted in fig. 6.5, where different signal types of an ideal transmitted waveform are distorted by the

Chapter 6 Multi-Gigabit Transmitter Σ C2 UI Delay C1 C0 C3 UI Delay UI Delay Dt-1 Dt Dt+1 Dt+2 Vout Din

Figure 6.6: Example of a 4-tap feed forward equalizer using delayed and different

weighted versions of the input signal.

low-pass transmission channel. For a clock pattern the resulting waveform of summed Single Bit Responses (SBR) is different compared to the channel response of one pulse, sent after many zero bits. Thus, ISI is data dependent and the distortion of one bit is deterministic for a defined pattern. It depends on the preceding and subsequent bits, and therefore also on the line coding, since it limits the maximum sequence length of consecutive equal symbols, like 8b/10b coding. Since ISI is a linear and time-invariant effect, an inverse filter can be added to the transmitter using pre-emphasis, to compensate the channel characteristics and mitigate ISI.

Since noise and crosstalk rather depend on layout implementation than on design techniques, the main architectural approach lies on DCD and ISI mitigation. The duty cycle balancing, which has been examined within the clock architecture development, is out of the scope of this thesis, but can be found in [68].

Regarding ISI, equalization can be used to effectively open the eye, but at de- creasing overall signal swing. In a transmitter a Feed Forward Equalizer (FFE) is typically employed to compensate variations in the SBR and improve signal quality. It utilizes a Finite Impulse Response (FIR) filter, which summarizes delayed versions of the input signal with a series of different tap weights, like depicted in fig. 6.6. Thereby the emphasis of the signal is done by boosting the higher frequency content and decreasing the lower frequency content, while the transmitted power is always kept constant.

6.2 Architecture R R IC0 Dt-1 VDD GND IC1 GND IC2 GND Vout Dt-1 Dt Dt Dt+1 Dt+1

Pre Main Post

(a) CML FFE. A R R A A A VDD VDD GND GND Pre Pre Main Main Main Main Main Post (b) SSTL FFE.

Figure 6.7: Simplified diagrams of a 3-tap FFE built-up with CML or SSTL

drivers.

The output signal for a 4-tap FFE is described by

Vout = C0· Dt−1+ C1· Dt+ C2· Dt+1+ C3· Dt+2 (6.1)

while

| C0 |+ | C1 |+ | C2 |+ | C3 |= 1 (6.2) with

C0 ≤0 and C2 ≤0 (6.3)

where Dx is the particular delayed digital input signal bit and Vout a nearly

continuous value. The input data signals are called pre cursor (Dt−1), main cursor

(Dt) and post cursor (Dt+1, Dt+2). The equalization coefficients Cn, determining

the tap weight, should allow a fine grain configuration to achieve the desired equalization resolution. If there are no limitations regarding the allocation of tap weights, a 4-tap FFE can also be configured for PAM4 encoding.

If it comes to the implementation with the line driver, there are noticeable differences between CML and SSTL, like depicted in fig. 6.7. A realization of an FEE with current mode logic is quite simple and can be built-up with switched current sources, where the adjusted current in a tail represents the particular tap coefficient. The advantage is, that the impedance does not vary with the equalizer settings, and only delayed signals have to be assigned to the circuit. The downside is, that the whole circuit has to run with the full rate. In comparison, a FFE with source series terminated logic has to be built-up with several driver segments, which are individually assigned to a particular cursor, as a function of the equalizer

Chapter 6 Multi-Gigabit Transmitter

settings. In a SST driver equalization can only be realized with a large number of individually assignable driver segments, while the total impedance is the sum of all resistors connected in parallel. Therefore, in case of a CML driver, resistor process variations just need to be adjusted at a single point. For a SSTL driver every segment needs to be terminated by itself and must allow resistor tuning. To gain a higher emphasis resolution, segments can be weighted binary and need to be calibrated individually for every group of the same weight, while assuming no process gradient within one TX lane.