Patent Publication Number: US-11652459-B2

Title: Differential amplifier circuitry

Description:
CROSS-REFERENCE OF RELATED APPLICATIONS 
     This application is a divisional under 35 U.S.C. § 111(a) of U.S. patent application Ser. No. 16/894,590, filed on Jun. 5, 2020, which in turn claims the benefit of European Patent Application No. 19178397.6, filed on Jun. 5, 2019, the entire disclosures of which Applications are incorporated by reference herein. 
    
    
     The present invention relates to differential amplifier circuitry, in particular to differential source follower circuitry. 
     By way of background,  FIG.  1    is a schematic diagram of previously-considered source follower circuitry  1 . The source follower circuitry  1  comprises an input transistor  2  (M 1 ) and a bias transistor  4  (Mb), both of which are n-channel field-effect transistors (e.g. NMOS transistors) in this example. An input voltage signal (Vin) is applied to the gate terminal of the input transistor  2  (M 1 ), and an output voltage signal (Vout) is taken from its source terminal. The drain terminal of the bias transistor  4  (Mb) is connected to the source terminal of the input transistor  2  and its source terminal is connected to ground  6 . The drain terminal of the input transistor  2  (M 1 ) is connected to VDD  8  (a voltage reference or voltage supply). A bias voltage is applied to the gate terminal of the bias transistor  4  in order to control the bias point of the input transistor  2 . The bias transistor  4  (Mb) acts as a current source, controlling a bias current flowing through the two transistors  2 ,  4 . The source follower circuitry  1  presents a high impedance to a preceding circuit stage and this is one reason why such source follower circuitry may be used as a voltage buffer. 
     As explained in more detail later, it has been found that such source follower circuitry suffers from gain loss due to channel length modulation (CLM) effects and limited output impedance of the input transistor  2  and the bias transistor  4 . The linearity of the source follower circuitry  1  is also degraded due to the CLM effect and variation in the output impedance with respect to the input signal. 
     It is desirable to address such problems. 
     According to an embodiment of a first aspect of the present invention, there is provided differential amplifier circuitry (or differential circuitry, or differential source follower circuitry) configured to generate a differential output signal between first and second output nodes based on a differential input signal provided between first and second input nodes, the circuitry comprising: first and second main transistors of a given conductivity type; and first and second auxiliary transistors of an opposite conductivity type to the given conductivity type, wherein the first and second main transistors are connected along first and second main current paths which pass between first and second main voltage reference nodes and the first and second output nodes, respectively, with their source terminals connected to the first and second output nodes, respectively, and with their gate terminals connected to be controlled by component input signals of the differential input signal provided at the first and second input nodes, respectively; and the first and second auxiliary transistors are connected along first and second auxiliary current paths which pass between first and second auxiliary voltage reference nodes and the first and second output nodes, respectively, with their drain terminals connected to the first and second output nodes, respectively, and with their gate terminals connected to be controlled by the component input signals of the differential input signal provided at the second and first input nodes, respectively. 
     Thus, the cross coupling configuration of the first and second auxiliary transistors leads to increased gain and improved linearity without any additional power consumption. Further details of the associated advantages are provided later herein. 
     The gate terminals of the first main transistor and the second auxiliary transistor may be connected directly to the first input node. 
     The gate terminals of the second main transistor and the first auxiliary transistor may be connected directly to the second input node. 
     The gate terminals of the first and second auxiliary transistors may be controlled by intermediate circuitry which is connected between the gate terminals of the first and second auxiliary transistors and the second and first input nodes, respectively. 
     The component input signals of the differential input signal may be a first and second input signal provided at the first and second input nodes, respectively. The first input signal may be inversely proportional to the second input signal. The first and second input signals may be directly input to the first and second input nodes, respectively. 
     The differential input signal may be provided by an input voltage supply. 
     The gate terminals of the first main transistor and the second auxiliary transistor may be directly controlled by the first input signal provided at the first input node. The gate terminals of the second main transistor and the first auxiliary transistor may be directly controlled by the second input signal provided at the second input node. 
     The first and second output nodes may be connected directly to the first and second main current paths, respectively. 
     The first and second main voltage reference nodes may be connected directly to the first and second main current paths, respectively. 
     The first and second output nodes may be connected via first and second combined current paths to first and second common voltage reference nodes, respectively. 
     Current flowing in the first combined current path may be a first current combination comprising (a sum of) currents flowing from (or in) the first auxiliary current path and the first main current path. 
     First and second current sources may be connected along the first and second combined current paths, respectively, whereby a first sum of currents flowing in the first main current path and the first auxiliary current path flows in the first combined current path and is controlled by the first current source, and whereby a second sum of currents flowing in the second main current path and the second auxiliary current path flows in the second combined current path and is controlled by the second current source. 
     Current flowing in the second combined current path may be a second current combination comprising (a sum of) currents flowing from (or in) the second auxiliary current path and the second main current path. 
     The first and second current sources may be or comprise first and second bias transistors, respectively. 
     The first current source may regulate the first sum of currents, and optionally a DC component of the first sum of currents; and the second current source may regulate the second sum of currents, and optionally a DC component of the second sum of currents. 
     The first and second current sources may regulate DC components of the first and second sums of currents to be the same as one another. Where there are pairs of first and second corresponding transistors and/or impedances, the transistors and/or impedances of each pair may be matched or have substantially the same configuration (e.g. sizes, dimensions, parameter values) as one another. 
     The first and second current sources may control the first and second sums of currents to be substantially constant (in particular, to have substantially constant DC components). That is, the first and second sums of currents may be controlled to remain at first and second predetermined current (DC) values, respectively. The combined value of the first and second predetermined (DC) current values may constitute a maximum (DC) power consumption value of the differential amplifier circuitry. 
     The first and second main voltage reference nodes may be connected to a main voltage supply (e.g. VDD 1 ); the first and second auxiliary reference nodes may be connected to an auxiliary voltage supply (e.g. VDD 2 ): and the first and second common reference nodes may be connected to a common voltage reference or supply (e.g. GND). 
     The main voltage supply and the auxiliary voltage supply may be referred to as the main voltage reference and the auxiliary voltage reference, respectively. 
     The main and auxiliary voltage supplies may provide the same voltage as one another, and are optionally the same voltage reference or supply as one another; or the main and auxiliary voltage supplies may provide different voltages from one another. 
     The first and second main transistors may be NMOS (or n-channel) transistors; the first and second auxiliary transistors may be PMOS (or p-channel) transistors; the main and auxiliary voltage supplies may provide high voltages and the common voltage reference or supply may provide a low voltage. 
     The first and second main transistors may be PMOS (or p-channel) transistors; the first and second auxiliary transistors may be NMOS (or n-channel) transistors; the main and auxiliary voltage supplies may provide low voltages and the common voltage reference may provide a high voltage. 
     The source terminals of the first and second auxiliary transistors may be connected (e.g. directly) to the first and second auxiliary voltage reference nodes, respectively. 
     The source terminals of the first and second auxiliary transistors may be connected to the first and second auxiliary voltage reference nodes, respectively, via respective first and second impedances. 
     The first and second impedances may each comprise a resistor connected between the source terminals of the first and second auxiliary transistors and the first and second auxiliary voltage reference nodes, respectively. 
     The first and second impedances may each further comprise a capacitor connected in parallel with the resistor. 
     First and second intermediate transistors of the given conductivity type may be connected along first and second intermediate current paths which pass between first and second intermediate voltage reference nodes and first and second common voltage reference nodes, respectively, with their source terminals connected to the first and second common voltage reference nodes, respectively, and with their gate terminals connected to be controlled by the component input signals of the differential input signal provided at the second and first input nodes, respectively; and first and second diode-connected transistors of the opposite conductivity type may be connected along the first and second intermediate current paths with their gate terminals connected to the gate terminals of the first and second auxiliary transistors, respectively, so that the first diode-connected and auxiliary transistors form a first current mirror and so that the second diode-connected and auxiliary transistors form a second current mirror. 
     The first and second diode-connected transistors may be configured such that their gate terminals are directly connected to their drain terminals. 
     The source terminals of the first and second intermediate transistors may be connected to the first and second common voltage reference nodes, respectively, via respective first and second impedances. 
     The first and second impedances may each comprise a resistor connected between the source terminals of the first and second intermediate transistors and the first and second common voltage reference nodes, respectively. 
     The first and second impedances may each further comprise a capacitor connected in parallel with the resistor. 
     The source terminals of the first and second diode-connected transistors may be connected (e.g. directly) to (the) first and second intermediate voltage reference nodes, respectively. 
     The first and second main voltage reference nodes may be connected to a main voltage supply; the first and second auxiliary reference nodes may be connected to an auxiliary voltage supply; the first and second intermediate reference nodes may be connected to an intermediate voltage supply; and the first and second common reference nodes may be connected to a common voltage reference or supply. 
     The main voltage supply, the auxiliary voltage supply and the intermediate voltage supply may be referred to as the main voltage reference, the auxiliary voltage reference and the intermediate voltage reference, respectively. 
     At least two of the main, intermediate and auxiliary voltage supplies may provide the same voltage as one another, and are optionally the same voltage supply as one another. 
     A differential output node may be connected to the first output node and the second output node, wherein a difference between the first sum of currents and the second sum of currents is output from the differential output node. 
     As a second aspect, differential amplifier circuitry may comprise a first main transistor of a first conductive type, whose source is connected to a first output node, whose gate is connected to a first input node, and whose drain is connected to a first voltage source line; a first auxiliary transistor of a second conductive type which is opposite to the first conductive type, whose drain is connected to the first output node, whose gate is connected to a second input node, whose source is connected to a second voltage source line; a second main transistor of the first conductive type, whose source is connected to a second output node, whose gate is connected to the second input node, and whose drain is connected to the first voltage source line; and a second auxiliary transistor of the second conductive type, whose drain is connected to the second output node, whose gate is connected to the first input node, and whose source is connected to the second voltage source line. 
     According to an embodiment of a third aspect of the present invention, there is provided programmable gain amplifier circuitry comprising the differential amplifier circuitry according to the aforementioned first or second aspect of the present invention. 
     According to an embodiment of a fourth aspect of the present invention, there is provided integrated circuitry such as an IC chip comprising the differential amplifier circuitry according to the aforementioned first or second aspect of the present invention or the programmable gain amplifier circuitry according to the aforementioned third aspect of the present invention. 
    
    
     
       Reference will now be made, by way of example, to the accompanying drawings, of which: 
         FIG.  1    is a schematic diagram of previously-considered source follower circuitry; 
         FIG.  2    is a graph useful for understanding output conductances of transistors in the circuitry of  FIG.  1   ; 
         FIG.  3    is a graph useful for understanding transconductance of an input transistor in the circuitry of  FIG.  1   ; 
         FIG.  4    is a graph useful for understanding variation of small signal AC gain of the circuitry of  FIG.  1   ; 
         FIG.  5    presents graphs useful for understanding variation of small-signal gain (bottom graph) with respect to the input signal (top graph) of the circuitry of  FIG.  1   ; 
         FIG.  6    is a schematic diagram of pseudo differential source follower circuitry; 
         FIG.  7    is a graph of an example differential output of the circuitry of  FIG.  6   ; 
         FIG.  8    is a graph of a Fast Fourier Transform (FFT) of the differential output of  FIG.  7   ; 
         FIG.  9    is a schematic diagram of differential amplifier circuitry according to an embodiment of the present invention; 
         FIG.  10    is a schematic diagram useful for understanding the  FIG.  9    circuitry; 
         FIG.  11    is another schematic diagram useful in understanding the  FIG.  9    circuitry; 
         FIG.  12    is a graph useful for understanding transconductances of transistors in the circuitry of  FIG.  9   ; 
         FIG.  13    is a graph useful for understanding small signal single-ended gain of the circuitry of  FIG.  9   ; 
         FIG.  14    is a graph of an FFT of an output signal of the  FIG.  9    circuitry; 
         FIG.  15    is a graph of an FFT of a differential output of the  FIG.  9    circuitry; 
         FIG.  16    is a schematic diagram of a variation of the differential amplifier circuitry of  FIG.  9   ; and 
         FIG.  17    is a schematic diagram of integrated circuitry embodying the present invention. 
     
    
    
     Before considering an embodiment of the present invention, the source follower circuitry of  FIG.  1    will be considered in more detail. 
     The gain A V  of the source follower circuitry  1  illustrated in  FIG.  1    can be calculated using small signal model analysis, as follows: 
                     A   V     =         V   out       V   in       =       g     m   ⁢           ⁢   1           g     m   ⁢           ⁢   1       +     g     o   ⁢           ⁢   1       +     g   ob                   (   1   )               
where g m1  is the transconductance of the input transistor  2 , g o1  is the output conductance of the input transistor  2  and g ob  is the output conductance of the bias transistor  4 . Vin is the input signal and Vout is the output signal as mentioned earlier.
 
     In large-signal applications, the transconductance and especially the output conductances of the transistors vary significantly with respect to the signal amplitude. This creates a variation of the gain A V  as a function of the input signal, represented as A V (Vin), and generates an output signal represented as:
 
 V   out   =A   V ( V   in )× V   in   (2)
 
     The variation of gain as a function of the input signal, as illustrated in equation (2), creates harmonic distortion in the output signal. 
     Furthermore, when the input signal increases the output signal also increases thereby causing the drain-source voltage of the input transistor  2  to reduce. Due to the CLM effect, a reduction in the drain-source voltage causes the output conductance g o1  to increase. On the other hand, the drain-source of the bias transistor  4  increases when the input signal increases, which causes the output conductance g ob  to reduce. The relationship between input signal and the transistor conductances is illustrated by equation (3):
 
 V   in   =V   in.max   :g   o1   =g   o1,max  and  g   ob   =g   ob,min   (3)
 
     Conversely, when the input signal reduces the output conductance of input transistor  2  reduces and the output conductance of the bias transistor  4  increases. This relationship is illustrated by equation (4):
 
 V   in   =V   in.min   :g   o1   =g   o1.min  and  g   ob   =g   ob,max   (4)
 
     Equations (3) and (4) indicate that the summation of the output conductances (i.e., g o1 +g ob ) varies roughly as a parabola with respect to the input signal, as illustrated by the graph of  FIG.  2   . 
       FIG.  2    is a graph which illustrates (for the source follower circuitry  1 ) variation of the summation of the above output conductances normalised to the common mode value (i.e. (g o1 +g ob )/(g o1 +g ob ) min  along the y-axis) with respect to the input signal, which is also normalised to the common mode value (i.e., V in /VICM along the x-axis), where VICM is the common mode input voltage value. That is, the value 1 indicates the normalised common mode value on both axes. The results illustrated by  FIG.  2    were obtained by simulation in 16 nm FinFET (Fin Field-Effect Transistor) technology. 
     The summation of output conductances illustrated in  FIG.  2    indicates that the variation of the gain, illustrated by equation (1), follows effectively the same parabola pattern with respect to the input signal. 
     Another notable feature of the source follower circuitry  1  is that if the bias current controlled by the bias transistor  4  (Mb) is relatively stable with respect to the input signal, the relative variation of the input transistor transconductance is much less than the transistor output transconductances.  FIG.  3    is a graph showing (for the source follower circuitry  1 ) variation in the input transistor transconductance normalised to the common mode (CM) value (i.e. g m1 /g m1,CM  along the y-axis) with respect to the input signal, which is also normalised to the common mode value (i.e. V/VICM along the x-axis). As with  FIG.  2   , the results illustrated by  FIG.  3    were obtained by simulation in 16 nm FinFET technology. 
     As illustrated by  FIG.  3   , the relative changes in the input transistor transconductance is around 2% compared to around 200% variation of the transistor output conductances shown in  FIG.  2   . This further indicates that the variation of the gain, as illustrated by equation (1), follows effectively the same parabola pattern as in  FIG.  2   . That is, variation of the gain is mainly dominated by the output conductance variation. 
       FIG.  4    is a graph which illustrates (for the source follower circuitry  1 ) variation of small signal AC gain with respect to the input signal normalised to the common mode value (i.e. V in /VICM). As with  FIGS.  2  and  3   , the results illustrated by  FIG.  4    were obtained by simulation in 16 nm FinFET technology. 
     As illustrated by  FIG.  4   , the gain of the source follower circuitry  1  has a similar parabola profile to that of the summed output conductances illustrated in  FIG.  2   . The parabola profile of  FIG.  4    indicates that in a case where a single tone sine wave is used as the input Vin of the source follower circuitry  1 , the gain varies as shown in  FIG.  5   . 
       FIG.  5    presents graphs which illustrate (for the source follower circuitry  1 ) variation of the small-signal gain (bottom graph of  FIG.  5   ) with respect to the variation of the input signal (top graph of  FIG.  5   ), where the input signal is normalised to the common mode value (i.e., V in /VICM). As with  FIGS.  2 ,  3  and  4   , the results illustrated by  FIG.  5    were obtained by simulation in 16 nm FinFET technology. 
     The results illustrated by  FIGS.  4  and  5    indicate that the small signal gain of the source follower circuitry  1  can be represented as follows:
 
 A   V   =A   V0   +av ( V   in   2 )  (5)
 
where A V0  is the constant term and av(V in   2 ) is the input signal dependent term of the gain. Based on equation (5), the output signal can be expressed as follows:
 
 V   out   =V   in   ×A   V   →V   out =( A   V0   ×V   in )+( V   in   ×av ( V   in   2 ))  (6)
 
     The second term in equation (6) (in particular the term av(Vin 2 )) shows the non-linearity of the output signal, which can be represented with an n-order polynomial, as follows:
 
 a   v ( x )=α 1   .x+α   2   .x   2 +α 3   .x   3 + . . .  (7)
 
     Substituting equation (7) into equation (6) gives the following equation:
 
 V   out =( A   V0   ×V   in )+(α 1   .V   in   3 +α 2   .V   in   5 +α 3   .V   in   7 + . . . )  (8)
 
     Equation (8) indicates that applying a single tone sine wave as an input Vin to the source follower circuitry  1  of  FIG.  1    causes third, fifth and subsequent odd order harmonics to be present in the output signal. When the source follower circuitry  1  is arranged in a differential structure, as illustrated in  FIG.  6   , the odd order harmonics are also present in the fully differential output: VOUTP−VOUTN. 
       FIG.  6    illustrates source follower circuitry  10 , which effectively comprises two sets of the source follower circuitry  1 . 
     The source follower circuitry  10  comprises a first input transistor  12  (MI 1 ), a second input transistor  22  (MI 2 ), a first bias transistor  14  (MB 1 ) and a second bias transistor  24  (MB 2 ), all of which are n-channel field-effect transistors (e.g. NMOS transistors) in this example. 
     The source follower circuitry  10  receives first and second input signals (VIP, VIN) at the gate terminals of the first and second input transistors  12 ,  22 , respectively. The second input signal may be considered inversely proportional to the first input signal. The first and second input signals are amplified by the first and second input transistors  12 ,  22 , respectively, and are output as first and second output signals (VOUTP, VOUTN) from corresponding first and second output nodes (source terminals of the first and second input transistors  12 ,  22 ), respectively. 
     The drain terminal of the first bias transistor  14  (MB 1 ) is connected to the source terminal of the first input transistor  12  (MI 1 ) and its source terminal is connected to ground  16 . The drain terminal of the first input transistor  12  (MI 1 ) is connected to AVD  18  (a voltage reference or voltage supply). A bias voltage VB is applied to the gate terminal of the first bias transistor  14  (MB 1 ), in line with  FIG.  1   . The drain terminal of the second bias transistor  24  (MB 2 ) is connected to the source terminal of the second input transistor  22  (MI 2 ) and its source terminal is connected to ground  26  (which corresponds to ground  16 ). The drain terminal of the second input transistor  22  (MI 2 ) is connected to AVD  28  (which corresponds to AVD  18 ). The bias voltage VB is applied to the gate terminal of the second bias transistor  24  (MB 2 ), again in line with  FIG.  1   . Thus, the first and second bias transistors  14  and  24  are biased in the same way, leading to substantially equal bias currents. 
     Operation of the source follower circuitry  10  will thus already be understood in line with the operation of the source follower circuitry  1 . The difference between the first and second output signals may be considered the output from the source follower circuitry  10 , and is effectively dependent on the difference between the first and second input signals (VIP, VIN). Thus, the source follower circuitry  10  may be referred to as differential source follower circuitry. Of course, it is evident from  FIG.  6    (by comparison with  FIG.  1   ) that VOUTN is dependent on VIN (irrespective of VIP), and VOUTP is dependent on VIP (irrespective of VIN), and with this in mind the source follower circuitry  10  may be referred to as pseudo differential source follower circuitry. 
     The pseudo differential source follower circuitry  10  may be used, merely for example, as a buffer to buffer the output of a switched-capacitor circuit.  FIG.  7    is a graph which illustrates the differential output (VOUTP-VOUTN) of the source follower circuitry  10  when operating as a buffer following the switched-capacitor circuit. The differential output is generated based on a single tone input provided by the switched-capacitor circuit. The amplitude of the differential output signal is normalised to the maximum input amplitude along the y-axis, with time along the x-axis. As earlier, the results illustrated by  FIG.  7    were obtained by simulation in 16 nm FinFET technology. 
       FIG.  8    is a graph which shows a Fast Fourier Transform (FFT) of the differential output illustrated in  FIG.  7   , with signal level in dB along the y-axis and frequency in MHz along the x-axis. In particular, the third (HD 3 ) and fifth (HD 5 ) harmonics spurs are identified in  FIG.  8   , which are present due to the non-linearity of the circuit as explained earlier. Based on these results, the effective resolution of the output signal in terms of effective number of bits (i.e., ENOB) is around 9.3 bits in the example simulation. 
     Due to the CLM effects and limited output impedance of the transistors in the pseudo differential source follower circuitry  10 , the circuit suffers from gain loss. Furthermore, as discussed above, the odd order harmonics present in the output signal illustrate the non-linearity of the pseudo differential source follower circuitry  10 . In order to mitigate gain loss and improve linearity of the pseudo differential source follower circuitry  10 , an embodiment of the present invention introduces an auxiliary circuit to the pseudo differential source follower circuitry  10 , as illustrated in  FIG.  9   . 
       FIG.  9    is a schematic diagram of differential amplifier circuitry  300  according to an embodiment of the present invention, comprising main circuitry  306  and auxiliary circuitry  308 . 
     The main circuitry  306  (which corresponds to the circuitry in  FIG.  6   ) comprises a first main transistor (M 1 P)  102  and a second main transistor (M 1 N)  202  connected along first and second main current paths  124 ,  224  which pass between first and second main voltage reference nodes  108 ,  208  and first and second output nodes  116 ,  116 , respectively. The source terminals of the first and second main transistors  102 ,  202  are connected to the first and second output nodes  116 ,  216 , respectively. The gate terminals of the first and second main transistors  102 ,  202  are connected to first and second input nodes  106 ,  206 , respectively. The drain terminals of the first and second main transistors  106 ,  206  are connected to a main voltage supply  312  (VDD 1 ) via the first and second main voltage reference nodes  108 ,  208 , respectively. 
     The auxiliary circuitry  308  (which is not present in  FIG.  6   ) comprises a first auxiliary transistor (MAN)  104  and a second auxiliary transistor (MAP)  204  connected along first and second auxiliary current paths  110 ,  210  which pass between first and second auxiliary voltage reference nodes  112 ,  212  and the first and second output nodes  116 ,  216 , respectively. The drain terminals of the first and second auxiliary transistors  104 ,  204  are connected to the first and second output nodes  116 ,  216 , respectively. The gate terminals of the first and second auxiliary transistors  104 ,  204  are connected to the second and first input nodes  106 ,  206 , respectively. The source terminals of the first and second auxiliary transistors  104 ,  204  are connected to an auxiliary voltage supply  314  (VDD 2 ) via the first and second auxiliary voltage reference nodes  112 ,  212 , respectively. 
     The main voltage supply  312  (VDD 1 ) and the auxiliary voltage supply  314  (VDD 2 ) could have the same voltage level as one another or different voltage levels. For example, the voltage level of the auxiliary voltage supply  314  (VDD 2 ) could be higher than the voltage level of the main voltage supply  312  (VDD 1 ) to provide more voltage headroom (i.e. allow a larger input voltage swing). 
     First and second impedances  114 ,  214  are connected along the first and second auxiliary current paths  110 ,  210  between the source terminals of the first and second auxiliary transistors  104 ,  204  and the first and second auxiliary voltage reference nodes  112 ,  212 , respectively. The impedances are (e.g. passive) electrical components which provide an impedance to current flowing along the first and second auxiliary current paths  110 ,  210 . The impedances may be or comprise, for example, degeneration resistors, or shunt capacitors (not shown) connected in parallel with degeneration resistors. By providing shunt capacitors in parallel with degeneration resistors along the first and second auxiliary current paths  110 ,  210 , the auxiliary circuit provides additional gain boosting of high frequency input signals. 
     The degeneration resistors could be implemented as a switched array of resistors (i.e. a variable resistor), so that the resistance values can be controlled to control the performance of the overall circuitry  300 . 
     The differential amplifier circuitry  300  further comprises first and second current sources  118 ,  218  connected along first and second combined current paths  120 ,  220  which extend between the first and second output nodes  116 ,  216  and first and second common voltage reference nodes  122 ,  222 , respectively. The first and second current sources  118 ,  218  are therefore configured such that a first sum of currents flowing in the first main current path  124  and the first auxiliary current path  110  flows in the first combined current path  120  and is controlled by the first current source  118 , and a second sum of currents flowing in the second main current path  224  and the second auxiliary current path  210  flows in the second combined current path  220  and is controlled by the second current source  218 . 
     The first and second common voltage reference nodes  122 ,  222  are connected to a common voltage reference or supply  310 , in this case ground supply (GND). 
     The first and second current sources  118 ,  218  may be first and second bias transistors configured to provide a substantially constant and substantially equal (DC) bias current flowing along the first and second combined current paths  120 ,  220 , respectively. In the present embodiment, the first current source  118  is implemented as a transistor (Mbp) which corresponds to the first bias transistor  14  (MB 1 ) in  FIG.  6   . Similarly, the second current source  218  is implemented as a transistor (Mbn) which corresponds to the second bias transistor  24  (MB 2 ) in  FIG.  6   . The transistors of the first and second current sources  118 ,  218  are matched and controlled at their gate terminals by a common bias voltage (VB), again in line with  FIG.  6   , leading to the substantially equal bias currents. 
     The transistors  102 ,  202 ,  118 ,  218  are n-channel field-effect transistors (e.g. NMOS transistors) in the present embodiment. The transistors  104 ,  204  are p-channel field-effect transistors (e.g. PMOS transistors), i.e. of an opposite conductivity type to transistors  102 ,  202 ,  118 ,  218 . Of course, the differential amplifier circuitry  300  could be provided “the other way up”, swapping p-channel devices for n-channel devices, and vice versa. The skilled person will appreciate that this applies equally to  FIGS.  1  and  6   . 
     Operation of the differential amplifier circuitry  300  will now be explained with reference to first and second subcircuits  302 ,  304  illustrated in  FIG.  10   , which presents the circuitry  300  in simplified form. Each subcircuit comprises elements of the main circuitry  306  and the auxiliary circuitry  308 , as discussed below. 
     The first subcircuit  302  comprises the first current source  118 , the first main transistor  102 , which receives a first input signal (VINP) from the first input node  106 , the first auxiliary transistor  104 , which receives a second input signal (VINN) from the second input node  206 , and the first impedance  114 . In the case of fully differential operation, when the first input signal VINP increases (causing the magnitude of the gate-source voltage of the first main transistor  102  to increase) the second input signal decreases (causing the magnitude of the gate-source voltage of the first auxiliary transistor  104  to also increase). 
     The first and second input signals are generated by an input voltage signal (not shown). The relationship between the first input signal, the second input signal and the input voltage signal is illustrated, as follows:
 
 V   in   =V IN P−V IN N   (9)
 
where V in  is the input voltage signal, VINP is the first input signal and VINN is the second input signal.
 
     The input voltage single may alternatively be referred to as a differential input signal, and the first and second input signals may alternatively be referred to as component input signals of the differential input signal. 
     The first impedance  114  provides a substantially linear voltage to current conversion for the first auxiliary transistor  104 . So, as the source-gate voltage of the first auxiliary transistor  104  increases, the current flowing through the first auxiliary transistor  104  increases in a substantially linear relationship to the input voltage (V in ). 
     Since the first current source  118  provides a constant current flowing along the first combined current path  120 , the bias current of the first main transistor  102  decreases with a substantially linear relationship to the input voltage. So, the bias current of the first main transistor  102  is proportional to 
               1     V   in       ,         
while the bias current of the first auxiliary transistor  104  is proportional to Vi. That is, the first current source  118  controls the bias current of the first main transistor  102  to be inversely proportional to the bias current of the first auxiliary transistor  104  in order that the summation of currents flowing through the first combined current path  120  remains constant. By controlling the summed currents to be constant in the first combined current path  120 , the first current source  118  ensures that the auxiliary circuit components of the first subcircuit  302  do not affect the power consumption of the differential amplifier circuitry  300  (i.e. no additional power is consumed by the auxiliary circuit components).
 
     The second subcircuit  304  comprises the second current source  218 , the second main transistor  202 , which receives the second input signal from the second input node  206 , the second auxiliary transistor  204 , which receives the first input signal from the first input node  106 , and the second impedance  214 . The second subcircuit  304  operates in a similar manner to the first subcircuit  302 . That is, the second current source  218  controls the bias current of the second main transistor  202  to be inversely proportional to the bias current of the second auxiliary transistor  204  in order that the summation of currents flowing through the second combined current path  220  remains constant. As with the first subcircuit  302 , by controlling the summed currents to be constant in the second combined current path  220 , the second current source  118  ensures that the auxiliary circuit components of the second subcircuit  302  do not affect the power consumption of the differential amplifier circuitry  300 . 
     In order to illustrate how the relationship between bias current and input voltage can help to improved gain and linearity, a small signal AC model analysis of the first subcircuit  302  (i.e. a half circuit model) is discussed below, with reference to  FIG.  11   . 
       FIG.  11    illustrates a small signal AC model of the first subcircuit  302  ignoring the output conductances of the first main transistor  102  and the first auxiliary transistor  104 . Ignoring the output conductances of these transistors gives a simpler equation to discuss the operation of the circuit without compromising the concept which will be discussed below. In fact, the transconductances of the first main transistor  102  and the first auxiliary transistor  104  generate large signal variations which mask the variation of the output conductances of these transistors. 
     Small signal AC model analysis of the first subcircuit  302  results in the following gain equation: 
     
       
         
           
             
               
                 
                   
                     A 
                     V 
                   
                   = 
                   
                     
                       
                         Vout 
                         / 
                         2 
                       
                       
                         Vin 
                         / 
                         2 
                       
                     
                     = 
                     
                       
                         Vout 
                         Vin 
                       
                       = 
                       
                         1 
                         + 
                         
                           
                             
                               g 
                               
                                 m 
                                 , 
                                 MAN 
                               
                             
                             × 
                             g 
                           
                           
                             
                               g 
                               
                                 m 
                                 , 
                                 
                                   M 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                   ⁢ 
                                   P 
                                 
                               
                             
                             × 
                             
                               ( 
                               
                                 g 
                                 + 
                                 
                                   g 
                                   
                                     m 
                                     , 
                                     MAN 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     The second term in equation (10) shows the additional gain added to the first subcircuit  302  due to the auxiliary circuitry  308 . This additional gain ensures that the gain provided by the first subcircuit  302  is greater than 1. 
     As discussed above, the bias current of the first main transistor  102  is proportional to the inverse of the input voltage. Therefore, the transconductance of the first main transistor  102  is proportional to the inverse of the square root of the input voltage. These two relationships can be represented as follows: 
     
       
         
           
             
               
                 
                   
                     
                       I 
                       
                         M 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                         ⁢ 
                         P 
                       
                     
                     ∝ 
                     
                       1 
                       
                         V 
                         in 
                       
                     
                   
                   , 
                   
                     
                       g 
                       
                         m 
                         , 
                         
                           M 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           P 
                         
                       
                     
                     ∝ 
                     
                       1 
                       
                         
                           V 
                           in 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     The bias current of the first auxiliary transistor  104  is proportional to the input voltage, so the transconductance of the first auxiliary transistor  104  is proportional to the square root of the input voltage. These two relationships can be represented as follows:
 
 I   MAN   ∝V   in   ,g   m,MAN ∝√{square root over ( V   in )}  (12)
 
The contribution of the auxiliary circuit components to the additional gain, illustrated in equation (10), can be rewritten as follows:
 
     
       
         
           
             
               
                 
                   
                     G 
                     AUX 
                   
                   = 
                   
                     
                       
                         
                           g 
                           
                             m 
                             , 
                             MAN 
                           
                         
                         × 
                         g 
                       
                       
                         g 
                         + 
                         
                           g 
                           
                             m 
                             , 
                             MAN 
                           
                         
                       
                     
                     = 
                     
                       1 
                       
                         
                           1 
                           g 
                         
                         + 
                         
                           1 
                           
                             g 
                             
                               m 
                               , 
                               MAN 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     The physical components that contribute to the terms represented in equation (13) are the first and second impedances  114 ,  214  of the auxiliary circuitry  308  and the first auxiliary transistor  104  (i.e. the equivalent conductance of two series resistors R and 
               1     g     m   ,   MAN         ,         
which is called G AUX ).
 
     According to equation (12), it can be expected that:
 
 G   AUX ∝√{square root over ( V   in )}  (14)
 
     The gain of the first subcircuit  302 , illustrated by equation (10) above, can be rewritten as follows: 
     
       
         
           
             
               
                 
                   
                     A 
                     V 
                   
                   = 
                   
                     1 
                     + 
                     
                       
                         G 
                         AUX 
                       
                       
                         g 
                         
                           m 
                           , 
                           
                             M 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                             ⁢ 
                             P 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     Considering the relationships illustrated by equations (11) and (14), it can be seen that the additional gain in (15), which is illustrated by the term 
                 G   AUX       g     m   ,     M   ⁢           ⁢   1   ⁢   P           ,         
varies proportionally to the input signal, as follows:
 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       A 
                       V 
                     
                   
                   = 
                   
                     
                       
                         G 
                         AUX 
                       
                       
                         g 
                         
                           m 
                           , 
                           
                             M 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                             ⁢ 
                             P 
                           
                         
                       
                     
                     ∝ 
                     
                       
                         
                           V 
                           in 
                         
                       
                       
                         1 
                         
                           
                             V 
                             in 
                           
                         
                       
                     
                     ∝ 
                     
                       V 
                       in 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     The term “ΔA V ” is the input voltage dependent term of the first subcircuit  302  gain. The relationship illustrated by equation (16) is the key to understanding the linearity of the differential amplifier circuitry  300  of  FIG.  9   . 
                     V   outp     =         A   V     ×     V   inp       =         (     1   +     Δ   ⁢           ⁢     A   V         )     ×       V   in     2       =         V   in     2     +     [     Δ   ⁢           ⁢       A   V     ⁡     (       V   in     2     )       ×       V   in     2       ]                   (   17   )               
where V outp  and V inp  are the AC signals of VOUTP and VINP (see  FIG.  9   ), respectively.
 
     The term 
             Δ   ⁢           ⁢       A   V     ⁡     (       V   in     2     )             
can be replaced with a first order polynomial as follows:
 
Δ A   V ( V   in )=β 0 +(β 1   ×V   in )  (18)
 
     Substituting equation (18) into equation (17) gives the following result: 
     
       
         
           
             
               
                 
                   
                     V 
                     outp 
                   
                   = 
                   
                     
                       
                         
                           V 
                           in 
                         
                         2 
                       
                       + 
                       
                         { 
                         
                           
                             [ 
                             
                               
                                 β 
                                 0 
                               
                               + 
                               
                                 ( 
                                 
                                   
                                     β 
                                     1 
                                   
                                   × 
                                   
                                     
                                       V 
                                       in 
                                     
                                     2 
                                   
                                 
                                 ) 
                               
                             
                             ] 
                           
                           × 
                           
                             
                               V 
                               in 
                             
                             2 
                           
                         
                         } 
                       
                     
                     = 
                     
                       
                         
                           
                             V 
                             in 
                           
                           2 
                         
                         + 
                         
                           ( 
                           
                             
                               
                                 β 
                                 0 
                               
                               × 
                               
                                 V 
                                 in 
                               
                             
                             2 
                           
                           ) 
                         
                         + 
                         
                           ( 
                           
                             
                               
                                 β 
                                 1 
                               
                               × 
                               
                                 V 
                                 in 
                                 2 
                               
                             
                             4 
                           
                           ) 
                         
                       
                       = 
                       
                         
                           [ 
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   β 
                                   0 
                                 
                               
                               ) 
                             
                             × 
                             
                               
                                 V 
                                 in 
                               
                               2 
                             
                           
                           ] 
                         
                         + 
                         
                           [ 
                           
                             
                               
                                 β 
                                 1 
                               
                               × 
                               
                                 V 
                                 in 
                                 2 
                               
                             
                             4 
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     Exactly the same maths holds for the second subcircuit  304  (i.e. the other half circuit), except the second input signal is inversely proportional to the first input signal (i.e. V in  is 
                 -       V   in     2       )     ,         
as follows:
 
     
       
         
           
             
               
                 
                   
                     V 
                     outn 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           - 
                           
                             ( 
                             
                               1 
                               + 
                               
                                 β 
                                 0 
                               
                             
                             ) 
                           
                         
                         × 
                         
                           
                             V 
                             in 
                           
                           2 
                         
                       
                       ] 
                     
                     + 
                     
                       [ 
                       
                         
                           
                             β 
                             1 
                           
                           × 
                           
                             V 
                             in 
                             2 
                           
                         
                         4 
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     The fully differential output AC signal can be represented as follows:
 
 V   out   =V   outp   −V   outn =(1+β 0 )× V   in   (21)
 
     As can be seen from equations (17) to (21), the non-linear term, which is due to the signal dependent gain, is the main source of second-order harmonics which cause second order distortion. This is contrary to the source follower circuitry  1  of  FIG.  1   , where odd order harmonics are generated, as illustrated in equation (8). 
     Due to the differential operation of the differential amplifier circuitry, the even order harmonics will eventually be removed, as illustrated in equation (21). Removal of these second-order harmonics significantly improves linearity and reduces distortion compared to source follower circuitry  1  or pseudo differential source follower circuitry  10 . 
     In order to further verify the effectiveness of the auxiliary circuitry  308  of the differential amplifier circuitry  300 , the circuit  300  of  FIG.  9    was simulated under the same test conditions as for the source follower circuit  1  of  FIG.  1   . The results of this simulation are illustrated in  FIGS.  12  to  15   , and were obtained by simulation in 16 nm FinFET technology. 
       FIG.  12    presents graphs which illustrate the transconductances of the first main transistor  102  and the first auxiliary transistor  104  with respect to the first input signal. The input transconductance of the first main transistor  102  (top graph of  FIG.  12   ) is normalised to its value at common mode voltage with respect to the (differential) input signal normalised to the input common mode voltage. The transconductance of the first auxiliary transistor  104  (bottom graph of  FIG.  12   ) is normalised to the transconductance of the first main transistor  102  at common mode voltage with respect to the normalised (differential) input signal. 
     Comparing the top and bottom graphs of  FIG.  12    illustrates that the transconductance of the first and second auxiliary transistors  104 ,  204  is a small fraction of the first and second main transistors  102 ,  202 . This results in just a small extra capacitive loading due to the auxiliary circuit on the input rails. 
       FIG.  13    illustrates the small signal single-ended gain of the differential amplifier circuitry  300  with respect to the (differential) input signal. Gain at the first output node  116  with respect to the input voltage is illustrated in the top graph of  FIG.  13   . Gain at the second output node  216  with respect to the input voltage is illustrated in the bottom graph of  FIG.  13   . 
     As can be seen in the two graphs of  FIG.  13   , there is a substantially linear relationship between the gain of the differential amplifier circuitry  300  with respect to the input voltage, as predicted in equation (16). 
     The two graphs of  FIG.  13    also illustrate some non-linear behaviour at extreme high and low values of the input voltage. This non-linear behaviour is mainly due to the variation and effect of the output conductances of the transistors  102 ,  202 ,  104 ,  204 , which are ignored in the aforementioned discussions. The output conductances introduce some higher-order terms in equation (18), which translates to higher order harmonics in the first and second output signals. However, as discussed below in relation to  FIG.  14   , the second-order harmonic of the differential amplifier circuitry  300  are removed in the fully differential output, which thereby reduces distortion and improves linearity. 
       FIG.  14    is a graph which shows an FFT spectrum of the first output signal of the differential amplifier circuitry  300 , in which a single tone sine wave is received at the first input node  106  as the first input signal, with signal level in dB along the y-axis and frequency normalised to the sampling frequency (i.e. f/f s ) along the x-axis. 
     A comparison of the FFT in  FIG.  14    to the FFT of  FIG.  8    illustrates a significant reduction in the third-order harmonic spur (HD 3 ) from −58 dB to −89.3 dB, while a second-order harmonic spur (HD 2 ) is introduced in the FFT of  FIG.  14   . As discussed above, this second-order harmonic spur is eventually removed in the fully differential output. 
       FIG.  15    is a graph which shows an FFT of the differential output from the differential amplifier circuitry  300 , with signal level in dB along the y-axis and frequency normalised to the sampling frequency (i.e. f/f s ) along the x-axis. As expected, the second-order harmonic is removed in the differential output, while the third-order (HD 3 ) and fifth-order (HD 5 ) harmonic spurs remain. The ENOB provided by the differential amplifier circuitry  300  in the present simulation is around 11.9 bits, which illustrates an enhancement to the linearity of the differential amplifier circuitry  300  of around 2.6 bits, compared to the pseudo differential source follower circuitry  10  of  FIG.  6   . 
     In overview, the  FIG.  9    circuitry allows enhancement of the source follower nonlinearity without imposing considerable power/area/loading penalty to the structure, and compensation of the gain loss of the circuit as a unity gain buffer. 
     By introducing an auxiliary circuit which is normally a small fraction of the main circuit, a small amount of gain is added to the signal path. This extra gain can compensate for the loss of the main circuit and provide gains more than 0 dB. The auxiliary circuit changes the profile of gain variation of the main circuit such that the variation is proportional to the input signal rather than the signal squared. This shifts the nonlinearity due to the gain variation (caused by the large-signal behaviour of the input signal) from a third-order distortion to a second-order distortion which will be removed in a fully differential architecture. The auxiliary circuit does not impose any extra power consumption to the structure, given that the overall bias current remains the same. Area wise, the auxiliary circuit is a small fraction of the main circuit. This minimises the extra loading on the input signal rails and consequently the loading on any preceding stages. 
       FIG.  16    is a schematic diagram of differential amplifier circuitry  400 , being a variation of the differential amplifier circuitry  300  of  FIG.  9   . 
     The differential amplifier circuitry  400  is similar to the differential amplifier circuitry  300 , and like elements have been denoted in the same way and duplicate description has been omitted. 
     The differential amplifier circuitry  400  differs from the differential amplifier circuitry  300  in that the auxiliary circuit  308  of the differential amplifier circuitry  400  further comprises intermediate circuitry. 
     In particular, the auxiliary circuit  308  further comprises first and second intermediate transistors  402 ,  502  connected along first and second intermediate current paths  404 ,  504  which pass between first and second intermediate voltage reference nodes  406 ,  506  and first and second common voltage reference nodes  122 ,  222 , respectively. The gate terminals of the first and second intermediate transistors  402 ,  502  are connected to be controlled by the component input signals of the differential input signal provided at the second and first input nodes, respectively. The source terminals of the first and second intermediate transistors  402 ,  502  are connected to the first and second common voltage reference nodes  122 ,  222 , respectively, via first and second impedances  410 ,  510 . The impedances  410 ,  510  may be or comprise, for example, degeneration resistors, or shunt capacitors (not shown) connected in parallel with degeneration resistors. By providing shunt capacitors in parallel with degeneration resistors along the first and second intermediate current paths  404 ,  504 , the auxiliary circuit  308  of the differential amplifier circuitry  400  provides additional gain boosting of high frequency input signals. 
     The auxiliary circuit  308  of the differential amplifier circuitry  400  further comprises first and second diode-connected transistors  408 ,  508  connected along the first and second intermediate current paths  404 ,  504  with their gate terminals connected to the gate terminals of the first and second auxiliary transistors  104 ,  204 . The first diode-connected and auxiliary transistors  408 ,  104  thereby form a first current mirror, and the second diode-connected and auxiliary transistors  508 ,  204  thereby form a second current mirror. The source terminals of the first and second diode-connected transistors  408 ,  508  are connected to first and second intermediate voltage reference nodes  506 ,  406 , respectively. 
     The first and second intermediate reference nodes  406 ,  506  are connected to an intermediate voltage supply  512 . The intermediate voltage supply  512  can be connected to the auxiliary voltage supply and/or the main voltage supply such that at least two of the voltage supplies provide the same voltage. Alternatively, all three voltage supplies may provide a different voltage. 
     The transistors  402 ,  502  are n-channel field-effect transistors (e.g. NMOS transistors) in the present embodiment. The transistors  408 ,  508  are p-channel field-effect transistors (e.g. PMOS transistors), i.e. of an opposite conductivity type to transistors  402 ,  502 . Of course, the differential amplifier circuitry  400  could be provided “the other way up”, swapping p-channel devices for n-channel devices, and vice versa. 
       FIG.  17    is a schematic diagram of integrated circuitry  600  embodying the present invention. The integrated circuitry  600  comprises the differential amplifier circuitry  300  described above. The integrated circuitry  600  could be a whole IC chip or be part of an IC chip. 
     As mentioned earlier in connection with the pseudo differential source follower circuitry  10 , the differential amplifier circuitry  300  may serves as a buffer to buffer the output of a switched-capacitor circuit. The switched-capacitor circuit could be a programmable gain amplifier. Thus, the integrated circuitry  600  could comprise the differential amplifier circuitry  300  and the switched-capacitor circuit, which in combination could be referred to as a programmable gain amplifier. 
     Circuitry of the present invention may be implemented as integrated circuitry, for example on an IC chip such as a flip chip. The present invention extends to integrated circuitry and IC chips as mentioned above, circuit boards comprising such IC chips, and communication networks (for example, internet fiber-optic networks and wireless networks) and network equipment of such networks, comprising such circuit boards. 
     The present invention may be embodied in many different ways in the light of the above disclosure, within the spirit and scope of the appended claims.