Continuous-Time Equalization

The continuous-time equalizers do equalization without the timing information.

The signal processed by continuous-time equalizer is not digitized. They always do equalization in the frequency domain. Since the characteristic of channel is usually a low-pass filter type, continuous-time equalizers are like high-pass filters to compensate or to equalize the frequency response of the channel. Hence, we can view the continuous-time equalizer as a high-pass filter. This equalizer has a trend of increasing gain in high frequency to compensate the gain loss of the channel. Using continuous-time equalizer between the channel and receiver, we expect the high pass response can just compensate the loss of channel at high frequency to flat or to

Chapter 3 Equalization Basis

equalize the total effective response. If we can not equalize the response, at least we can make frequency band nearly flat. Fig. 3.1 roughly illustrates the goal of this kind of equalizer.

Figure 3.1 Channel response and equalizer response.

However, any circuit has its poles and zeros. That means to reach infinite high gain at the infinite high frequency is impossible. Gain amount of frequency response will fall after an limited frequency range. Fig. 3.2 illustrates the practical frequency response of continuous-time equalizers. In this figure, we use piece-wise to sketch a roughly Bode plot. We assume there is a zero at a relative low frequency in the equalizer circuit. The response will increase in 20 dB/dec when there is a zero. The

Figure 3.2 Frequency response of continuous-time equalizers.

Chapter 3 Equalization Basis

gain keeps rising with the frequency increasing until reaching the first pole. The first pole cancels the rising frequency of the zero and flats the frequency response. As the frequency keeps increasing, the gain will drop dramatically due to the dominant pole introduced by the circuit itself.

Obviously, in order to compensate the loss of channel, continuous-time equalizers create the zero to produce a gain pulse in high frequency part. Allocating the first zero and first pole at proper frequency, we can move the gain pulse to the band we focus on. Although the effective response is not flat through the whole frequency, the equalizer extends the flat part toward the range of data transmission frequency.

A continuous-time equalizer is truly a simple one tap continuous-time circuit with high-frequency gain boosting transfer function that effectively flattens the channel response. The equalizer can be implemented by passive components or active components. As an example, the required frequency shaping can be achieved by a simple RC network as shown in Fig. 3.3. The resistor attenuates the low-frequency signals while the capacitor allows the high-frequency signal content, thus resulting in high frequency gain boosting. The transfer function and the pole zero frequencies are given by:

Figure 3.3 Continuous-time passive equalizer.

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The gain-boost factor is proportional to the ratio of zero and pole frequency ωp/ωz, so reasonable amounts of equalization can be achieved by choosing appropriate component values that set the required gain-boosting. There are two main drawbacks with simple passive RC equalizers. First, the RC network introduces large impedance discontinuity at the channel and equalizer. Employing inductors for impedance matching networks can be used to prevent the discontinuity. However, the large inductors make this approach less suitable for on-chip integration. Second, this method can not improve SNR since equalization is performed by attenuating low-frequency signal spectrum. Due to these reasons, this technique has limited use in high-speed serial links.

It is desirable to have a gain greater than one at all frequencies to maximize the benefit from receiver-side equalization. Therefore, equalizers using active circuit elements rather than passive components are required to achieve gains greater than one. Since parallel RC combination introduces a zero in the transfer function, it is possible to degenerate the transistors in a differential pair such that their effective transconductance increases at high frequencies [6][7][20]. Shown in Fig. 3.4, such an arrangement employs both capacitive and resistive degeneration. We express the equivalent transconductance as

Chapter 3 Equalization Basis

Figure 3.4 Continuous-time equalizer using capacitive degeneration.

where gm is the MOS (M1,M2) tranconductance. By designing the zero frequency to be lower than the dominant pole, considerable high frequency gain boosting can be achieved and it will looks like the frequency response in Fig. 3.2. However, the maximum gain boosting achieved by this method is limited by the bandwidth of the amplifier due to the load capacitance.

There are several other broadband techniques for equalizing filters proposed, like inductive peaking [20], Cherry Hopper amplifier [7], or combination of inductive peaking and Cherry Hopper amplifier [21]. The goal of these circuits is to widely extend the effective gain boosting in higher frequencies.

Unlike discrete-time equalizers (we will discuss in the Section 3.2), which need

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sampling clock to perform equalization, continuous-time equalizers just provide high-frequency boost to equalize the band. However, the gain-peaking transfer function of the equalizer amplifies the high frequency noise that degrades the noise margin. Moreover, the adaptation mechanism of continuous-time equalizers is more complex than that of discrete-time ones. These are disadvantages of continuous-time equalizers.