Complex Parallel-Series Reduction

1. Introduction

Silvaco’s Guardian LVS tool compares two circuits that are defined by their netlists. The comparison is based strictly on the topological structure of these circuits. Topologically equivalent netlists are considered different, even if they are functionally equivalent. There are several techniques available for designing the same functionality by means of topologically different netlists. While it is impossible for the LVS tool to "know" about all these techniques, many are supported.


2. Reduction Varieties

A general method of ignoring strict topological equivalence during the layout design phase is the disregarding of the order of series-connected transistors in the reduction phase. Series Reduction is a process of reducing series-connected, same-type transistors that feature different gate terminals. In order for LVS to properly handle this process, a special "pseudo-node" device is introduced into the netlist graph. This pseudo-node represents the series of transistors as a single node. The resulting logical configuration is called a cluster. Users choose to recognize or disregard series transistor order by checking the box next to "Series Reduction" in the Model Settings Panel (Figure 1). The option is set independently for each device type and model.

Figure 1. Model Settings Panel.


Another reduction process in the Guardian LVS tool is called parallel reduction. Parallel reduction is used to reduce parallel sets of transistors for later use in a separate series reduction. Parallel reduction also replaces sets of clusters that are connected in parallel and constructed previously from "pseudo-nodes." The logical configuration obtained as a result of parallel reduction is also called a cluster. Users choose to recognize or disregard parallel transistor order by checking the box next to "Parallel Reduction" in the Model Settings Panel (Figure 1). The option is set independently for each device type and model.

Since the LVS tool handles sets of parallel transistors without reducing to single "pseudo-node," parallel reduction must be activated in tandem with series reduction. In addition, the series reduction feature is also used to reduce either a series of parallel clusters or a series of both transistors, as well as parallel clusters that are connected in series form to a single cluster.


3. Simple Abstraction Model for Reduction

The section describes a simple reduction-stage abstraction model that helps to illustrate some problems that arise during the process. Figure 2 is an illustration of a series-parallel network of MOSFET transistors. Transistors M1 and M3 and gates G1 and G3 are connected in parallel, as are transistors M2 and M4 and gates G2 and G4. Transistor pairs M1-M3 and M2-M4 are connected in series. There is no way for series reduction to transform this schematic if parallel reduction is not previously executed.

Figure 2. Series-parallel network
of MOSFET transistors.

Note: Gates G1 and G3 nets should not be identical. Identical gates result in a "transistor parallel merging" pattern. The transistors are merged if the box next to the "Parallel Merge" option of Guardian LVS’s Model Settings Panel (see Figure 1) is checked. Necessary merging is automatic if the Series Reduction and Parallel Reduction options are turned on, regardless of the state of the Series Merge or Parallel Merge settings.

How are parallel and series reduction performed? A relatively simple abstraction model for handling different reduction cases is illustrated by Figure 3.

Figure 3. Reduction for series-parallel
network using simple abstraction model.


After a combination of parallel and series reductions, the original network is replaced by single cluster with interchangeable G1, G2, G3 and G4 gate terminals. Pseudo-nodes in Figure 3 are indistinguishable from other pseudo-nodes obtained from the network shown in Figure 4, because Figure 4 is also reduced to a single cluster of interchangeable G1, G2, G3 and G4 gate terminals:

Figure 4. Reduction for parallel-series
network using simple abstraction model.


It is necessary to improve the abstraction model to distinguish the two previous cases, but to do so is complicated. It is possible that in both netlists in some place we have the configuration from previous figure. Let’s assume that net G1 in Figure 3 is connected to a network with local characteristic A. Net G2 is connected to the network with characteristic B, G3 to network C, and G4 to network D. Let’s assume also that net G1 in Figure 4 is connected to the network with characteristic A, G2 to C, G3 to B, and G4 to D. There is no difference between these configurations because in this abstraction model, G2 and G3 are not interchangeable.


4. Guardian LVS Abstraction Model for Reduction

The Guardian LVS matching engine abstraction model accurately reflects conditions of gate terminal interchangeability, and to solve problems like the one found in section 3. For the previous example it is possible to interchange G1 and G2, G3 and G4, as well as pairs G1-G2 and G3-G4. An idea for an abstraction model that met our requirements is illustrated in Figure 5.

Figure 5. Reduction for parallel-series
network realized in Guardian LVS tool.

In this model, several "pseudo-devices" and "pseudo-net" nodes represent the original network. Pseudo-nets are represented as PN1, PN2 and PN3. Pseudo-devices are shown as "gate-arrays" GA1, GA2, GA3 and cluster CL1. Each gate-array represents single interchangeability: GA1 provides interchangeability of G1 and G2, GA2 makes G3 and G4 interchangeable, and GA3 makes the pairs G1-G2 and G3-G4 interchangeable as well. If the matching engine finds an error in pseudo-node GA1, GA2, GA3, PN1, PN2, PN3, or CL1, it is reported to the user in transistor cluster M1-M4.

Reduction process for network of Figure 2 can be illustrated in Figure 6.

Figure 6. Reduction for series-parallel network realized in Guardian LVS tool.


In Figure 6, cluster CL1 is the result of a series reduction of "pseudo-devices" that was executed after the parallel reduction of transistor pairs M1, M3 and M2, M4.



Guardian LVS from Silvaco features several options for both parallel and series transistor reduction. These reductions improve interchangeability and help to reduce many of the problems associated with transistor reduction.



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