Abstract:
Methods and circuits are disclosed for low voltage (1.5 Volt and below) CMOS circuits, offering good transconductance and current driving capabilities. These goals are achieved by biasing CMOS transistors in the weak inversion region, by utilizing multiple unit-sized transistors with a fixed gate width to gate length ratio, and by maintaining a uniform threshold voltage of each unit-sized transistor. The required transistor size is obtained by parallel connection of several unit-sized transistors, such that `n` unit sized transistors carry the required current of `n` units. The methods and circuits disclosed eliminate deviation of the output current of current mirrors caused by threshold voltage mismatch. Disclosed are a current mirror and two typical amplifiers as examples of weak inversion design.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates to biasing of CMOS circuits, and more particularly to avoiding problems with biasing, current mismatch, low transconductance, and sizing of circuits in the weak inversion region. 
     2. Description of the Related Art 
     It is well known that the main hurdle for low voltage (1.5V and below) circuit operation is the metal oxide semiconductor (MOS) transistor threshold voltage. Fortunately there exists a region of operation for the MOS transistor which allows low voltage operation. This is the so-called &#34;sub-threshold&#34; or &#34;weak inversion&#34; region. In this region, the transistor can be made to operate at a gate-source voltage of about 200 mV below the threshold voltage as compared to about 200 mV above it for the normal or the &#34;strong inversion&#34; region of operation. Also, the drain current saturation voltage in weak inversion region is also low--less than 100 mV compared to typically 200 mV for strong inversion. Therefore it is easy to see that the weak inversion region of operation provides opportunities for designing low voltage circuits. 
     FIG. 1a shows a conventional prior art current mirror in strong inversion with unequal sized transistors. The drain and source of an n-channel transistor NR0 are shown connected between a current supply I --  IN and the gate is shown connected to the drain, creating a current source. N-channel transistor NR1 has its drain and source connected between I --  OUT and ground, and its gate is connected to the gate of transistor NR0. NR1, thus acts as a current mirror, conducting a current of n times the current I flowing into transistor NR0, because NR1 has a width n times wider than transistor NR0. 
     FIG. 2a shows a conventional prior art common source amplifier in strong inversion. P-channel transistors PR0 and PR1 act as a current source/mirror, similar to transistors NR0 and NR1 of FIG. 1a. PR1 supplies a current I to output OUT, equal to the current flowing through PRO to input IBIAS --  IN. N-channel transistor NR1, the common source amplifier, is connected between output OUT and ground and receives at its gate a bias voltage and signal input BIAS+SIGNAL which is to be amplified. R o  is the resistance seen at the output. The voltage gain is given by: ##EQU1## where g m1  =transconductance of NR1 R o  output resistance of PR1 and NR1 in parallel. 
     FIG. 3 shows a prior art differential input amplifier in strong inversion. The current mirror is identical to the one of FIG. 2a, except that PR1, the current mirror, has twice the width of PRO to deliver twice the current (2I) of PR0. The differential amplifier consists of differential inputs INP and INM which each feed the p-channel transistor gate of a first and second CMOS circuit comprised of PRA1/NRA1 and PRB1/NRB1, respectively. NRA1 is a current source for current mirror NRB1. Each string PRA1/NRA1 and PRB1/NRB1 conduct current I. The output OUT has an output resistance of R o . The voltage gain is given by: ##EQU2## where gm 1  =transconductance of PRB1 R o  =output resistance of PRB1 and NRB1 in parallel. 
     The problems associated with weak inversion operation are firstly, absence of a design guideline for biasing the transistor in the correct region of operation, secondly the drain current mismatch for unequal sized current mirrors and thirdly very low transconductance and current driving capabilities. All these problems are resolved in the invention maintaining requirements of low voltage operation. 
     There are two papers which treat the subject of weak inversion operation. The first paper is by Eric Vittoz and Jean Fellrath, titled CMOS Analog Integrated Circuits Based on Weak Inversion Operation, IEEE Journal of Solid-State Circuits, Vol. SC-12, NO. 3, June 1977. The second paper is by Tim Grotjohn and Bernd Hoefflinger, titled A Parametric Short-Channel MOS Transistor Model for Subthreshold and Strong Inversion Current, IEEE Journal of Solid-State Circuits, Vol. SC-19, NO. 1. February 1984. 
     The following three U.S. Patents have come to our attention which utilize circuits that use biasing in the weak inversion region. U.S. Pat. No. 5,047,706 (Ishibashi et al.) describes a constant current, constant voltage circuit in which two of the MOS devices are operated in a sub-threshold region, however, there does not appear to be any discussion of the invention&#39;s deviation in output current. U.S. Pat. No. 4,792,749 (Kitagawa et al.) describes a voltage regulator for a solar cell in which a CMOS current mirror is operated in the weak inversion region. U.S. Pat. No. 4,555,623 (Bridgewater et al.) discloses a pre-amplifier for a focal plane detector array in which the devices are operated in a weak inversion region. 
     It should be noted that none of the above-cited examples of the related art provide multiple unit sized CMOS transistors avoiding threshold voltage mismatch and deviation of the output current. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide methods and circuits for low voltage (1.5 Volt and below) applications, offering good transconductance and current driving capabilities. 
     Another object of the present invention is to eliminate deviation of the output current of current mirrors caused by threshold voltage mismatch. 
     A further object of the present invention is to provide examples of the application of weak inversion design in the form of two typical amplifiers. 
     These objects have been achieved by biasing CMOS transistors in the weak inversion region, by utilizing multiple unit-sized transistors with a fixed gate width to gate length ratio, and by maintaining a uniform threshold voltage of each unit-sized transistor. The required transistor size is obtained by parallel connection of several unit-sized transistors, such that `n` unit sized transistors carry the required current of `n` units. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     FIG. 1a is a circuit diagram of a current mirror of the prior art. 
     FIG. 1b is a circuit diagram of a current mirror of the present invention. 
     FIG. 2a is a circuit diagram of a common source amplifier and current mirror of the prior art. 
     FIG. 2b is a circuit diagram of a common source amplifier and current mirror of the present invention. 
     FIG. 3 is a circuit diagram of a differential input amplifier and current mirror of the prior art. 
     FIG. 4 is a block diagram illustrating the method of providing a differential input amplifier and current mirror of the present invention. 
     FIG. 5 is a high level circuit block diagram of a differential input amplifier and current mirror of the present invention. 
     FIG. 6 is a detailed circuit diagram of a differential input amplifier and current mirror of the present invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     We will start with the current equation for weak inversion region of operation for the MOS transistor which is as follows: 
     
         I.sub.D =I.sub.T ·exp[(V.sub.GS -V.sub.T0)/α·V.sub.T ]·[1-exp (-V.sub.DS /V.sub.T) ]                                                         (1) 
    
     Where 
     
         I.sub.T =μ·C.sub.OX (W/L)·αV.sub.T.sup.2 (2) ##EQU3## 
    
     
         φ.sub.F =V.sub.T ·ln(N.sub.A /n.sub.i)        (4) 
    
     
         δ=γ=√(2qε.sub.SI N.sub.A)       (5) 
    
     
         V.sub.T =kT/q                                              (6) 
    
     
         α=1+C.sub.D /C.sub.OX                                (7) 
    
     
         C.sub.OX =ε.sub.ox /t.sub.OX                       (8) 
    
     I D  =Drain current. 
     V GS  =Gate-source voltage. 
     V DS  =Drain-source voltage. 
     I T  =Corner value of current for weak to strong inversion transition. 
     V T0  =Threshold voltage. 
     μ=Carrier mobility. 
     C D  =Depletion Capacitance under gate per unit area. 
     C OX  =Gate capacitance per unit area. 
     φ F  =Fermi potential. 
     N A  =Substrate doping concentration. 
     n I  =Intrinsic carrier concentration of silicon. 
     γ=Body factor. 
     ε SI  =Permittivity of silicon. 
     ε OX  =Permittivity of silicon dioxide. 
     t OX  =Gate oxide thickness. 
     V T  =Thermal voltage. 
     α=Slope factor. 
     k=Boltzmann&#39;s constant. 
     T=Temperature in deg. Kelvin. 
     q=Electronic charge. 
     W=Width of gate. 
     L=Length of gate. 
     Careful observation of (1) yields that I D  must be less than I T  for V GS  to be less than V T0  which is necessary for sub threshold or weak inversion operation. In fact, (1) is no longer valid if I D  is larger than I T  as the device enters strong inversion region. From (1) and (2) this restriction can be expressed as: 
     
         I.sub.D &lt;I.sub.t                                           (1a) 
    
     or, ##EQU4## 
     Again examining (1) we can see that I D  saturates if V DS  is greater than 3V T  which is about 78 mV at room temperature. For analog applications, we need to operate in this region only, therefore (1) simplifies to: 
     
         I.sub.D =I.sub.T ·exp[(V.sub.GS -V.sub.T0)/α·V.sub.T ]                     (9) 
    
     The small signal transconductance g m  of the device is obtained from (9) as: 
     
         g.sub.m =δI.sub.D /δV.sub.GS =I.sub.D /α·V.sub.T (10) 
    
     Examining (10) we see that g m  is independent of the aspect ratio W/L. Therefore the aspect ratio must be determined from other considerations. From (9) we have: 
     
         V.sub.GS =V.sub.T0 -α·V.sub.T ·ln(I.sub.T /I.sub.D) (11) 
    
     or ##EQU5## 
     The sizing of a transistor in weak inversion should be done using (11a), keeping in mind the restriction in (2a). One has to decide on a value for W/L and a value of I D  to obtain a small size and an acceptable value of V GS  for low voltage operation keeping in mind that only the ratio I D  :W/L is important. Henceforth we will refer to this value of W/L as the &#34;unit size&#34; and this value of I D  as one unit current. The ratio of I D  :W/L found suitable is typically 20 nA, but may range from 1 nA to 300 nA for an n-channel transistor and is about three times lower for a p-channel transistor. 
     Typical values for several of the parameters for a 0.25 μm CMOS process are: 
     μC OX  ·αV T   2  =300 nA for n-, and 100 nA for p-channel transistor, 
     V TN  =0.5V, 
     V TP  =0.6V, 
     α·V T  =33.8 mV, 
     Applied to (11a) we get the values listed in Tables 1 and 2. 
     
                       TABLE 1______________________________________for n-channel transistorI.sub.D /(W/L)     I.sub.D        W/L    V.sub.GS______________________________________20      nA       100    nA     10/2 0.408V1       nA       5      nA     10/2 0.307V300     nA       1.5    μA  10/2 0.500V______________________________________ 
    
     
                       TABLE 2______________________________________for p-channel transistorI.sub.D /(W/L)     I.sub.D        W/L    V.sub.GS______________________________________6.67    nA       100    nA     30/2 0.508V0.33    nA       5      nA     30/2 0.407V100     nA       1.5    μA  30/2 0.600V______________________________________ 
    
     The choice of V GS  depends on the minimum power supply of operation. The minimum power supply is equal to: 
     
         V.sub.GSN V.sub.GSP +2V.sub.Dsat, 
    
     where 2V Dsat  =100 mV 
     For 1 Volt operation, V GSN  =0.4V and V GSP  =0.5V will be good values; the corresponding I D  and W/L values are given in the Tables above. 
     All unit-sized transistors are assumed to be identical in all respects--this can be ensured to a large extent by careful layout considerations. In the following discussions we will see that any other size will be obtained by parallel connection of several unit-sized transistors. Thus a composite transistor which carries a current of say `n` units of current must have `n` unit transistors such that each unit transistor carries one unit current. A unit size of a PMOS will be three times that of an NMOS since mobility of the former is one third of that of the latter. This also follows from (11a). 
     FIG. 1a shows a current mirror in the strong inversion with unequal sized transistors. Using (11) and (9) one can show that the current mirror should work similarly in the weak inversion. However it is observed that the latter exhibits a lot of deviation for the output current from the theoretically predicted value. This is due to the difference in threshold voltages as a result of size difference of the transistors. The V GS  -I D  relationship obeys the square law in strong inversion but is exponential in weak inversion. Therefore the effect of threshold voltage mismatch is more prominent in weak inversion. 
     This problem can be solved using one unit-sized transistor for the smaller transistor and several unit-sized transistors in parallel for the bigger transistor of the mirror. The solution is shown in FIG. 1b. Each unit-sized transistor carries one unit current. 
     From (2) we can see that the value of I T  for the unit transistor is quite small because V T  is a small quantity. This results in poor g m  and current driving capabilities in weak inversion as can be seen from (10). These difficulties can be overcome using parallel connected unit-sized transistors carrying one unit current, each, to replace those transistors that must have large g m  or must be biased at high currents for large driving capability. The advantage of this arrangement is that while the composite transistor operates at a high current, each individual unit-sized transistor still operates in the weak inversion carrying one unit current. Therefore the composite transistor still exhibits the same low voltage characteristic (in terms of V GS  and minimum V DS  for current saturation). The g m  of the composite transistor is the sum of those of the individual unit-sized transistors, therefore, good values of g m  s can be obtained. This happens because the drain currents of the unit transistor add up to constitute the total current while all of them have the same gate voltage. 
     With the description above it may seem that the chip area required to achieve g m  s of the same order as in strong inversion will be enormous as the ratio of the current level in strong inversion and the unit current in weak inversion is very large. However, in fact, the situation is not so alarming. The analysis below proves the argument. 
     In strong inversion transconductance g ms  at drain current I DS  is given by: ##EQU6## 
     The same in weak inversion is given by (10) assuming I D  is one unit current. Now, let us say N unit-sized devices need to be connected in parallel to achieve the same amount of transconductance as in strong inversion, then using (12) and (10) we have: ##EQU7## From the above equation and (2) we can show that: ##EQU8## Also, from (13) we have: ##EQU9## 
     Now α is close to unity as C D  is much smaller than C OX  as can be seen from (7). Also, I T  is usually one or two orders of magnitude smaller than I DS . Therefore, from (13) we can see that: 
     
         N&lt;&lt;I.sub.DS/I.sub.D                                        (14) 
    
     and from (13a): ##EQU10## 
     Interpreting (14) and (14a) we can see that neither the area nor the power consumption required to achieve the same transconductance as in strong inversion, by connecting multiple transistors in weak inversion, is as high as we would expect. 
     Some examples of the application of this idea are shown in FIG. 2b and FIG. 6. It is worthwhile mentioning here that the above technique may be also be applied to portions of the entire circuit, different portions of the circuit having different unit sizes and unit currents to optimize area. But the basic sizing and biasing procedure remains the same as described. 
     Referring now to FIG. 1b, we begin a description of the method and circuit of a current mirror of a preferred embodiment the present invention. FIG. 1b shows a current mirror utilizing W/L unit-sized n-channel transistors. This circuit can be converted to a p-channel current mirror by &#34;mirroring&#34; it along the reference potential (or ground rail), by replacing the n-channel transistors with p-channel transistors, and by connecting the source of the p-channel transistors to a voltage potential (typically V dd ). Please compare FIG. 1a and FIG. 2a for this &#34;mirroring&#34;. We will use the term `CMOS transistor` to refer to either circuit. 
     The method of providing a current mirror operating in the weak inversion region, comprises the steps of: 
     providing a first CMOS transistor NO with a source-drain path and a gate and connecting it between a first terminal of a current supply (I --  IN) and a second terminal of that current supply, thereby creating a current source; 
     providing `n` second CMOS transistors (ranging from N1 to Nn) having the same gate size as the first CMOS transistor N0; 
     connecting the gate and the source of each of these `n` second CMOS transistors to the gate and the source of the first CMOS transistor, respectively; 
     connecting the drains of these `n` second CMOS transistors together creates a current mirror; 
     biasing the first CMOS transistor to operate in the weak inversion region by selecting a unit drain current I D  for the first CMOS transistor below the strong-to-weak inversion point of a CMOS transistor. 
     Each of these `n` second CMOS transistors is operating in the weak inversion region of a CMOS transistor because gate to source voltage and gate current are identical to those of the first CMOS transistor. The drain currents of the `n` second CMOS transistors add up to provide a total current equal to `n` times the drain current of each of the `n` CMOS transistors. The first and the `n` second CMOS transistors of the current mirror circuit have a gate width of W and a gate length of L, the ratio of W to L is called `unit size`. It is, of course, understood that the `unit size` of a p-channel transistor is one third of that of an n-channel transistor. The total transconductance g m  of all the `n` second CMOS transistors is the sum of the individual transconductance of each of the unit sized `n` second CMOS transistors. The ratio of unit drain current ID to unit size--I D  :(W/L)--is typically 20 nA, but ranges from 1 nA to 300 nA for an n-channel transistor. Analogous, the ratio of unit drain current I D  to the unit size for a p-channel transistor is typically 20/3 or about 7 nA, but ranges from 1/3 nA to 100 nA. The first CMOS transistor and the `n` second CMOS transistors operate with a drain-to-source voltage ranging from V DD  to less than 100 mV. 
     Referring now to FIG. 2b, we describe next the method and circuit of a common source amplifier of the preferred embodiment of the present invention. The circuit of FIG. 2b is comprised of a current source 21, a current mirror 22, and an amplifier part 23. The circuit of FIG. 2b can be converted to an n-channel current mirror and a p-channel amplifier by &#34;mirroring&#34; the circuit along the reference potential (or ground rail), by exchanging n-channel transistors with p-channel transistors, and by connecting the drain of the n-channel transistors to a voltage potential (typically V dd ) and the drain of the p-channel transistors to a reference potential (typically ground). Please compare FIG. 1a and FIG. 2a for this &#34;mirroring&#34;. 
     The method of providing a common source amplifier operating in the weak inversion region, comprises the steps of: 
     providing a current mirror as detailed above with reference to FIG. 1b and reference to &#34;mirroring&#34; and noting that the current mirror of FIG. 2b is shown implemented using p-channel transistors P0 as a current source 21 and p-channel transistors P1 to Pn as current mirror 22. The current for the drain of P0 is shown provided by input BIAS --  IN. The amplifier part 23 is provided by `n` n-channel transistors N1 to Nn, each having a source-drain path and a gate, the `n` n-channel transistors having the same gate size as p-channel transistor P0; 
     connecting the gates of each of the `n` n-channel transistors to an input node BIAS+SIGNAL which receives a bias voltage and signal input that is to be amplified; 
     connecting the sources of each of the `n` n-channel transistors to a reference potential (typically ground); and 
     connecting the drains of each of the `n` n-channel transistors to output node OUT. 
     and receives at its gate a bias voltage and signal input BIAS+SIGNAL which is to be amplified. 
     R o  is the resistance seen at output node OUT. The voltage gain is given by: 
     
         A.sub.v =V.sub.out/ V.sub.signal =g.sub.m1 ·R.sub.o 
    
     where g m1  =transconductance of N1 
     R o  =output resistance of N1 and P1 in parallel. 
     All transistors of the common source amplifier are biased to operate in the weak inversion region of a CMOS transistor by selecting a unit drain current I D  for the first CMOS transistor P0 below the strong-to-weak inversion point of a CMOS transistor. Drain currents of the `n` second p-channel transistors add up to provide a total current equal to `n` times the drain current of each of the `n` p-channel transistors. All `n` second p-channel and `n` n-channel transistors are biased to have the same gate voltage. All p-channel and n-channel transistors of the common source amplifier have a gate width of W and a gate length of L, where the ratio of W to L is called `unit size`. As already mentioned the `unit size` of a p-channel transistor is one third of an n-channel transistor. The ratio of unit drain current I D  to the unit size is typically 20 nA, but ranges from 1 nA to 300 nA for an n-channel transistor and one third for p-channel transistors. The common source amplifier provides a current amplification equal to `n` at the output node OUT. 
     Referring now to FIG. 4 we describe in a block diagram a method of providing a differential input amplifier operating in the weak inversion region. In Block 41 we operate a current source in weak inversion mode using a unit sized transistor, producing a unit current I D . In Block 42 a current mirror is connected to the current source of Block 41, where the current mirror has `n` unit sized transistors, all operating in weak inversion mode as well, where each transistor is producing a current I D . A current `n` times I D  is delivered in Block 43 at an output of the current mirror. In Block 44 an amplifier is connected to that output (in the presently discussed embodiment this is a differential input amplifier, however, this method is applicable to any other amplifier, as disclosed previously and shown in FIG. 2b), where each standard transistor of that amplifier is replaced by `n` unit sized transistors operating in weak inversion mode. 
     In further elaboration of the method of providing a differential input amplifier we wish to point out that the number of unit transistors provided in the current mirror is `2n`, because a differential input amplifier is comprised of two transistors one for each input, as can clearly be seen by reference to FIG. 3. Because each transistor requires a current `n` times I, the current mirror needs to provide a current of `2n` times I. 
     Next we give an overview of the circuit of the differential input amplifier in terms of the block diagram of FIG. 5. Block 51, the current source, and Block 52 receive input BIAS --  IN. Block 52 is connected through the Common Node to Block 53, the differential input stage, which receives inputs INP and INM and furnishes amplifier output OUT of the differential input amplifier. 
     We now offer, in FIG. 6, a detailed description of the differential input amplifier operating in the weak inversion region, where is transistor has a unit-sized ratio of W/L: 
     Current source 51 is a first p-channel transistor PI0 with a source-drain path and a gate, the source of the first p-channel transistor is connected to a voltage potential V dd , the gate and drain of the first p-channel transistor are connected to a biasing signal BIAS --  IN, where the first p-channel transistor provides a current source; 
     Current mirror 52 has a first input, a second input and a common node, the first input is connected to the gate of the first p-channel transistor, the second input is connected to the source of the first p-channel transistor, where current mirror 52 provides a source of current at the common node. The current mirror further comprises: 
     `2n` second p-channel transistors PIA1 to PIAn and PIB1 to PIBn, each transistor having a source-drain path and a gate, where the `2n` second p-channel transistors are all connected in parallel, gate and source of each of the `2n` second p-channel transistors connected to the first and second input of current mirror 52, respectively, and the drains of each of the `2n` second p-channel transistor connected to the common node of the current mirror; 
     Differential input stage 53 has plus input INP, minus input INM, a connection to the common node, and an amplifier output OUT, the differential input stage amplifies signals at INP and INM and provides an amplified signal at amplifier output OUT. The differential input stage further comprises: 
     a first set of `n` p-channel transistors PA1 to PAn, each having a source-drain path and a gate, the gates of each of the first set of `n` p-channel transistors connected to INP, the sources of each of the first set of `n` p-channel transistors connected to the common node, and the drains of each of the first set of `n` p-channel transistors connected to a node A; 
     a second set of `n` p-channel transistors PB1 to PBn, each having a source-drain path and a gate, the gates of each of the second set of `n` p-channel transistors connected to INM, the sources of each of the second set of `n` p-channel transistors connected to the common node, and the drains of each of the second set of `n` p-channel transistors connected to amplifier output OUT; 
     a first set of `n` n-channel transistors NA1 to NAn, each having a source-drain path and a gate, the gates and drains of the first set of `n` n-channel transistors connected to node A, the sources of the second set of `n` n-channel transistors connected to a reference potential GND (typically ground); and 
     a second set of `n` n-channel transistors NB1 to NBn, each having a source-drain path and a gate, the gates of the second set of `n` n-channel transistors connected node A, the sources of the second set of `n` n-channel transistors connected to reference potential GND, and the drains of each of the second set of `n` n-channel transistors connected to amplifier output OUT. The output OUT has an output resistance of R o . The voltage gain is given by: ##EQU11## where g m1  =transconductance of PB1, and R o  output resistance of PB1 and NB1 in parallel. 
     All p-channel and n-channel transistors of the differential input amplifier are biased to operate in the weak inversion region by selecting a unit drain current below the strong-to-weak inversion point of a CMOS transistor. 
     Advantages of this present invention are in summary: 
     circuit operation at voltages below 1.5 Volt 
     no drain current mismatch for unequal sized current mirrors 
     high transconductance and good current driving abilities 
     adaptable to various circuits and portions of circuits 
     different portions of a circuit can have different unit sizes and different unit currents to optimize silicon area 
     reasonable power consumption and area compared to prior art circuit operated in strong inversion. 
     While the invention has been particularly shown and described with reference to the preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made without departing from the spirit and scope of the invention.