Physical Methods of Speed-Independent Module Design
Oleg Izosimov
INTEC Ltd, Room 321, 7a Myagi Street, Samara 443093, Russia
1. Introduction
Any method of logic circuit design is based on using formal models
of gates and wires. The simplest model of a gate is determined by only two
"parameters": (a) Boolean function is to be calculated, (b) fixed
propagation delay. The simplest model of a wire is an ideal medium with
zero resistance and consequently, with zero delay. Such simple models allow
circuit design procedures which are a sequence of elementary steps easily
realized by a computer.
When logic circuits designed by using the simplest models expose
unreliable operation as in the case of gate delay variations, designers
introduce less convenient but more realistic models with arbitrary but
finite delay. Using more complicated models may produce logic circuits that
are called speed-independent [1].
In speed-independent circuits transition duration can be arbitrary.
So a centralized clock cannot be used. Instead special circuitry to detect
output validity is applied. Besides, additional interface circuitry is
needed to communicate with the environment in a handshaking manner. A speed-
independent circuit can be seen as a module consisting of combinational
logic (CL) proper, CL output validity detector (OVD) and interface
circuitry (Fig.1). To enable OVD to distinguish valid output data from
invalid ones, the redundant coding scheme was proposed [2]. The main idea
of the scheme is to enumerate all possible input and output data, both
valid and invalid. The OVD must be provided with appropriate information on
data validity. To realize the idea of redundant coding some constraints on
CL design are imposed [3]:
[pic]
(i) CL must be free of delay hazards, i.e. CL output data word must not
be dependent on the relative delay of signal paths through CL.
(ii) In changing between input states, any intermediate or transient
states that are passed through must not be mapped by CL onto valid output
states.
When these constraints were formulated, the circuit designers
realised that not every Boolean description could be implemented in a speed-
independent style. Other approaches to speed-independent module design were
needed.
SIM design as a science has two branches: logical and physical. For
a long time physical branch was overshadowed in spite of its
competitiveness. The main properties of physical approach to SIM design
are:
(a) Arbitrary coding scheme.
(b) Conventional procedure of operational unit design.
(c) Races of signals in SIM do not affect on its proper operation.
In this paper we propose an approach based on the physical nature of
transitions in CL. We believe that each transition is actually a transfer
of energy which can be naturally detected by physical methods.
From the viewpoint of a radio engineer CL behaves like a radio
transmitter. It emits radio frequencies in the 108-1010Hz band modulated by
signals of 106-108Hz. Obviously, the carrier wave is produced by gate
switchings during transitions in CL. The modulating wave is produced by
control schemes (OVD and interface circuitry) that detect transition
completion and inform the environment about the readiness of CL. OVD is a
kind of radio receiver that extracts the modulation envelope and enhances
the received signal. The main properties that OVD circuit must expose from
a radio engineer's point of view are selectivity and high gain. Since the
useful signals can propagate through non-conducting medium, OVD circuits
can be coupled with CL indirectly.
Advances in semiconductor technology gave birth to two methods of
transition detecting based on two kinds of the information carrying signal,
namely electromagnetic radiation and current consumption. Frequency of the
signal produced by switching logic gates is determined by gate delay.
For instance, CMOS network of 1-ns gates produces 1-GHz signal, ECL
array of 100-ps gates gives 10-GHz radiation. Logic circuits consisting of
10-ps gates will emit infra-red radiation. That signal could be easily
detected by photosensitive devices.
2. Background
Let us have a closer look at the structure of speed-independent
modules (SIM) as presented in Fig.1. All input data are processed in CL,
all output data are obtained from CL, too. So, CL is the only unit in SIM
which is involved in proper data processing. The result of that processing
is specified by Boolean functions. Algorithms for calculating the Boolean
function are realised by the internal structure of CL. Generally, its
structure is series-parallel as well as algorithm implemented.
When n-bit data word is put into the CL, n or more signal
propagation paths (SPPs) can be activated concurrently. So, one can say
that the calculation of a Boolean function by CL is of parallel nature. On
the other hand, each SPP is a gate chain which processes data in a serial
manner. So, calculation in CL is also of sequential nature.
The OVD circuit is intended for detecting transient and steady
"states" of CL. If any SPP in CL is still "active", CL is in transient
state, otherwise it is in steady state. Each gate switching results in both
logical and electromagnetic effects on its surrounding medium. The logical
effects of switching has been heavily investigated; we consider physical
one.
To provide speed-independence of the module the OVD and interface
circuitry must also work in a speed-independent mode. This means that any
arbitrary but finite transistor or wire delay cannot impair proper
operation of OVD and interface circuitry.
The interface circuitry is a mediator between OVD and environment of
SIM. It implements any kind of signalling convention, commonly a two- or
four-cycle one [4] based on request Req and acknowledgement Ack signal
using. The interface circuitry receives the output validity (OV) signal
from the OVD circuit, a Req signal from the environment and transmits an
Ack signal to the environment (Fig.1).
Consider an algorithm of operation for interface circuitry realizing
speed-independent four-cycle signalling convention (FCSC). In accordance
with FCSC the control signals must go in the following sequence: Req+OV-
Ack+Req-Ack- where "+" corresponds to rising the signal and "-" corresponds
to falling the signal. All signals are assumed to adhere to positive logic.
Initially the signals Req and Ack are low, the signal OV is high. If the
environment state changes, the Req signal rises and transient state of CL
occurs (OV-). Upon completion of the transitions in CL, signal OV rises and
the interface circuitry generates the Ack signal rising. After that the
environment produces a falling Req signal and then the interface circuitry
transmits the falling Ack signal to the environment. All the signals have
to be reset into the initial state.
To develop the interface circuitry a circuit designer must take into
account that any OVD circuit has finite (non-zero) turn-on delay ton. This
means that OVD cannot respond on transitions of short duration t tr< ton .
An example of interface circuitry is shown in Fig.2. It contains a
flip-flop, a NOR-gate, an asymmetrical delay and an inverter as an output
stage [5].
The asymmetrical delay is intended for delaying Req rising signal
for + period where + > ton . Delaying Req falling signal noted - is to be
as short as possible. Note that speed-independent operation of interface
circuitry is vulnerable to delay + variation. If + becomes less than ton ,
proper operation of SIM can not be guaranteed. Otherwise, if + is much
more than ton , performance of SIM will be significantly reduced. To
provide exact accordance of + and ton a circuit emulator can be used.
Such an emulator is either an exact copy of OVD or its functional
copy, i.e. resistive-capacitive model of OVD's critical path. In the chip
the emulator must be placed next to active OVD circuit in order to ensure
identical conditions of fabrication and operation.
In this example we use a simplified asymmetrical delay implemented
as an asymmetrical CMOS inverter chain (Fig.3). Contrary to the common
inverter an asymmetrical one has non-equal rise and fall times of output
signal.
A time diagram for interface circuitry is presented in Fig.4 for two
cases: (a) ttr < ton and (b) ttr ton. In case (a) the signal sequence
Req+Ack+ is formed for (++tNOR) period where tNOR is a NOR-gate delay. In
case (b) the above sequence is formed for (ttr +toff+tNOR) duration where
toff is a turn-off delay of OVD circuit. When the SIM returns to the
initial steady state, the signal sequence Req-Ack- is formed for (-+tNOR)
interval.
After considering the SIM in operation it is obvious that the main
problems of the module design are in the area of CL and OVD interaction.
This includes (a) kind of signal used as a carrier of information about CL
output validity, and (b) method of OVD circuit design.
4. Current consumption detection
Using current consumption of CMOS CL for output validity detection
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