Embodiments of the present invention relate to analog circuits, and more particularly, to discrete-time analog filters.
FIG. 1 provides a high-level abstraction of a portion of a computer server or system, where microprocessor 102 resides on board 104 and communicates with memory 106 on board 108. The communication is by way of striplines on backplane 110. Backplane 110 is connected to boards 104 and 108 by connectors 112. Not shown in FIG. 1 are other memory units and microprocessors, where the various microprocessors and memory units may communicate to one another so as to access or write data and instructions.
Communication of signals over backplane 110 may be modeled by transmission line theory. Often, the signaling is based upon differential signaling, whereby a single bit of information is represented by a differential voltage. For example, FIG. 2a shows drivers 202 and 204 driving transmission lines 206 and 208, respectively. For differential signaling, drivers 202 and 204 drive their respective transmission lines to complementary voltages. Typical curves for the node voltages at nodes n1 and n2 for a bit transition are provided in FIG. 2b, where the bit transition is indicated by a dashed vertical line crossing the time axis. The information content is provided by the difference in the two node voltages.
For short-haul communication, such as for the computer server in FIG. 1, the signal-to-noise ratio is relatively large. If the transmission lines are linear, time-invariant systems having a bandwidth significantly greater than that of the transmitted signal, then a relatively simple receiver architecture may be employed to recover the transmitted data. Such a receiver is abstracted by comparator 210, which provides a logic signal in response to the difference in the two received voltages at ports 212 and 214.
However, every transmission line has a finite bandwidth, and for signal bandwidths that are comparable to or exceed the transmission line (channel) bandwidth, intersymbol interference may present a problem. Furthermore, actual transmission lines may have dispersion, whereby different spectral portions of a signal travel at different speeds. This may result in pulse spreading, again leading to intersymbol interference. As a practical example, for high data rates such as 10 Gbs (Giga bits per second), the transmission lines used with backplanes or motherboards are such that intersymbol interference is present.
Channel equalization is a method in which a filter is employed at a receiver so as to equalize the channel. The use of digital filters for channel equalization is well known. However, digital filters for such applications require an analog-to-digital converter, which may be costly and difficult to implement at high data rates, and the digital filtering itself may be difficult to implement at high data rates. Consequently, there has been an interest in analog filters for channel equalization. The design of analog filters for channel equalization with high data rates such as 10 Gbs may be challenging. Furthermore, in many high performance applications, the supply voltage is scaling to lower and lower values. This further challenges the circuit designer because of the reduced voltage headroom.