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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].
[pic]
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.
[pic]
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.
[pic]
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
was proposed in 1990 [7]. Contrary to the method of EMR detection this one
is based on introducing direct coupling of source and receiver. While CL is
in steady state it consumes current of about 10-9-10-8A which does not
allow OVD switching. The interface circuitry gets information on CL output
validity and in turn informs the environment about CL readiness to input
data processing. When an input data arrives CL changes its state to
"transient", current consumption increases to 10-4-10-2A, which switches
the OVD, thus informing the interface circuitry about output invalidity.
The latter lets the environment know about CL business.
After the computations in the CL are finished, the current consumption
decreases down to the steady state value, and the OVD sends a signal of
output validity.
4.1 Information carrying signal
Current consumption by CMOS CL contains useful information on CL
state. CMOS CL is a network of CMOS gates, so the current consumed by CL is
a superposition of currents consumed by CMOS gates included in the CL.
Each CMOS gate contains PMOS transistor and NMOS transistor networks
(Fig.5). While a gate is in a steady state either the PMOS or the NMOS
network is in a conducting mode. When a gate switches the non-conducting
transistor network becomes conducting. There is usually a short period in
switching time when both networks are in a conducting mode.
[pic]
Generally, current consumed by a CMOS gate includes three
components [9,10]:
(a) leakage current Ilk passing between power supply and ground due
to finite resistance of non-conducting transistor network;
(b) short-circuit current Isc flowing while both networks are in a
conducting mode;
(c) load capacitance CL charge current ILC flowing while a CMOS gate
is switching from low to high output voltage via conducting PMOS network
and CL .
SPICE simulation has shown [5] that amplitude of current consumed by
a typical CMOS inverter depends on CL and is limited by the non-zero
resistance of the conducting PMOS network (Fig.7). The integral of consumed
current is proportional to CL . When a gate switches from high to low
output voltage, the component ILC is negative by direction and negligible
by value (Fig.7b). It is evident, the switchings from high to low output
voltage occur at the expense of energy accumulated in CL during the
previous switching from low to high output voltage. The component Isc does
not depend on direction in which a gate switches.
[pic]
[pic]
The component ILC equals to ILC = CLVdd f where Vdd is a power
supply voltage, f is a gate switching frequency. Veendrick has investigated
the component Isc dependencies on CL and rise-fall time of input potential
signal [10]. He showed that if both input and output signal have the same
rise-fall time, the component Isc cannot be more than 20 percent of summary
current consumption [10]. However, when the output signal rise-fall time is
less than input one, the component Isc can be of the same order of
magnitude as ILC. In that case it must be taken into account. As to the
component Ilk, it entirely depends on CMOS process parameters and for state
of the art CMOS devices Ilk is about 10-15 -10-12 A.
So, the analysis of CMOS gate current consumption allows us to
conclude that in transient state a CMOS gate consumes a current I=
Ilk+Isc+ILC and in steady state it consumes only Ilk<< I . The difference
between two states from the viewpoint of current consumption is several
orders of magnitude. So, CMOS gate output validity detection is possible,
both in principle and in practice.
In Section 2 we presented series-parallel model of computations in
CL. We showed that in every moment during switching current consumed by CL
is a superposition of the currents consumed on the activated signal
propagation paths (SPPs). Now, considering CL implemented by CMOS devices
we should note that while logical signal propagates through SPP the
neighbouring gates switch in opposite directions. That is why a curve of
current consumed by a ten inverter chain (Fig.8) looks like a combination
of crests and troughs. Nevertheless, in the very lowest point of the curve
the current consumed by CL in a transient state remains several orders more
than in a steady state.
[pic]
4.2 OVD implementation
The proposed OVD circuit, shown in Fig.9, is a threshold circuit
translating an analog current signal I into a logical signal OV.
[pic]
The OVD circuit contains a current-to-voltage converter (CVC)
consisting of the resistor R1 and the diode D1. The OVD also contains a
comparator implemented by the MOS transistors M1-M7 and resistors R2,,,R3 .
CMOS CL consumes the current I and introduces a capacitance Cin . The
capacitance Cout represents the load caused by the interface circuitry. A
low potential output signal of OVD corresponds to CL output validity. A
high potential output signal corresponds to CL output invalidity. So, OVD
generates OV signal in negative logic manner.
The transfer characteristics of CVC is determined by a system of
three equations:
[pic] [pic]
where I is an input current of CVC, V is a voltage drop on the CVC circuit,
Ir is a current flowing through the resistor R1, Id is a current passing
through the diode D1, I0 is a leakage current of the diode, rb is a bulk
resistance of the diode. Here [pic] stands for kT/q where k is Boltzmann's
constant, T is absolute temperature, q is charge of an electron.
Equations (1)-(3) determine the functional connection F between
input current I and voltage drop V: [pic]. Graphic solution of the system
is shown in Fig.10.
[pic]
CVC parameters to be calculated are R1 and rb. Initial data for
calculating R1 are the threshold voltage drop Vth and corresponding
threshold input current Ith . Value Ith is determined by minimal current
consumed by CMOS CL in transient state. Initial data for calculating rb are
maximal voltage drop Vmax and corresponding maximal input current Imax.
Value Imax is determined by the maximal number of gates in CL switching
simultaneously and their load capacitances.
The comparator chosen is the CMOS ECL receiver proposed by Chappell
et al.[11]. The circuit includes a single differential amplifier stage with
built-in compensation for parameter variations, followed by a CMOS
inverter. The comparator has 100-mV worst-case sensitivity in 1-m
technology. Detailed static and dynamic analysis of the comparator circuit
was given in [11].
The comparator compares input voltage signal Vin with reference
voltage Vref. If Vin Vref, the
comparator output signal equals to logical "one" which means that the
outputs are invalid.
As it follows from the OVD circuit configuration,
[pic] [pic]
where Vdd is a voltage of power supply.
Equations (4) and (5) allow us to calculate the threshold voltage
drop V of the CVC circuit:
since [pic], so [pic] [pic]
If 0<750mV, the diode D1 is in active mode and while rb <<20, the component under
the sign of summation in Equation (7) can be much larger than the
component Cin. Due to voltage drop V the effective power supply voltage is
reduced and CL performance is decreased by about 35 percent [7].
In order to make SIM operating faster special attention must be paid
to reducing the capacitance introduced by CL.
4.3 Speed-independent address bus
The simplest case of CL is a scheme degenerated into a set of wires
called a multi-bit bus. Let us develop the OVD circuit for such a CL.
Multi-bit bus consists of several lines. Each line can be
considered as a medium for signal propagating from one end of the chip
to another. Delay of signal propagation through a line depends on several
factors:
(a) output impedance and symmetry of driver circuit;
(b) initial state of the line: if driver is symmetrical, line switching
from high to low voltage lasts shorter than reverse switching;
(c) electrical properties of the line as a signal propagation medium
(resistance of conducting layer and capacitances between the line and other
wires next to it);
(d) length of the line;
(e) input impedance and sensitivity of receiving circuit.
Since different lines of the bus operate in different conditions
(a)-(e), signal propagation delays are different, too. From the standpoint
of environment the bus behaves like any other more complicated CL.
Asynchronous RAM designers use a bus transition detector since 1980s
[13-15]. Such a detector is usually based on double-rail address coding
and two series connected transistors for each address bit [15]. One of
the transistors receives the true address signal and the other receives
the complementary address signal of the particular address bit. For any
steady state condition one of the transistors will be turned on and one
will be turned off. There will be a finite rise and fall time during a
transition of the address bit. There is a short time during which both
transistors are conducting. The establishment of the conductive
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