Abstract:
A method and apparatus for amplifying signals is disclosed. In one embodiment, the apparatus comprises a first MOSFET having a drain, a source and a gate. The apparatus further comprises a second MOSFET having a drain, a source and a gate. The second MOSFET is a depletion mode device having a substantially greater drain saturation current than the first MOSFET. The drain of the first MOSFET is connected to the source of the second MOSFET through a first conductor, and the source of the first MOSFET is connected to the gate of the second MOSFET through a second conductor. Finally, the apparatus further comprises a conductor for connecting the drain of the second MOSFET to biasing source to apply sufficient voltage to cause saturation of the first and second MOSFETs.

Description:
BACKGROUND OF THE INVENTION 
     1. Technical Field 
     This invention relates to analog circuits, and more particularly concerns a method and apparatus for amplifying signals. 
     2. Description of the Related Art 
     Analog circuits are often used in a broad range of signal-processing applications such as analog-to-digital converters. Such converters generally use a plurality of amplifiers and resistors to produce a digital output in response to an analog input from physical motion detectors or electrical voltages. While the amplifiers used with such analog circuits may be of different types, several advantages associated with metal-oxide-semiconductor-field-effect-transistors (MOSFET) make MOSFETs potentially very useful in analog circuits. For example, MOSFETs typically have virtually infinite input resistance and zero offset voltage, both of which are important in terms of analog design. However, because MOSFETs typically have a relatively low open-loop gain and relatively low transconductance, bipolar junction transistors were generally preferred over MOSFETs for use in analog circuits. 
     Several methods for increasing the output resistance of transistors used in analog circuits have been developed. For example, in Csanky, &#34;Combing FET&#39;s for Higher Gains&#34;, Electronic Design, Sept. 27, 1963 at p. 36, the author discloses a circuit in which the source of a first junction field effect transistor (&#34;JFET&#34;) is connected to the drain of a second JFET, while the gate of the first JFET is connected to the source of the second JFET. By combining the JFETs in this manner, the output resistance of the pair of JFETs is greater than the output resistance of each of the JFETs individually. Because open-loop gain is a function of the transconductance of a circuit multiplied by the output resistance, the open-loop gain of the JFETs collectively also was greater than each JFET individually. See also Csanky, U.S. Pat. No. 3,271,633. Another method for increasing the output resistance of MOSFETs is described in Grey et al., &#34;MOS Operational Amplifier--A Tutorial Overview&#34;, IEEE Journal of Solid State Circuits, v. SC-17, n. 6, December 1982. In this reference, a cascode circuit using four MOSFETs is disclosed in which the output resistance and hence the open-loop gain is increased. 
     The references discussed above well illustrate the void in the art associated with amplifiers used in analog circuits. Methods which used MOSFETs generally required a relatively large number of components to achieve the desired gain. In addition, the methods which used JFET suffered from the disadvantages of having relatively small increase in output resistance as well as having low input resistance. For example, the output resistance of JFET circuits using the method described above was typically 50 Mohms. 
     SUMMARY OF THE INVENTION 
     According to the preferred embodiment of the present invention, a method and apparatus for amplifying signals is disclosed. In one embodiment, the apparatus comprises a first MOSFET having a gate for receiving input signals as well as a drain and a source. The apparatus further comprises a second MOSFET having a drain, a source and a gate. The second MOSFET is a delpetion mode device having a substantially greater drain saturation current than the first MOSFET. The drain of the first MOSFET is connected to the source of the second MOSFET through a first conductor, while the source of the first MOSFET is connected to the gate of the second MOSFET through a second conductor. Finally, the apparatus further comprises a conductor for connecting the drain of the second MOSFET to a biasing source to apply sufficient voltage to cause saturation of the first and second MOSFETs. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The various advantages of the present invention will become apparent to one skilled in the art by reding the following specification and by reference to the drawings in which: 
     FIG. 1 is a schematic diagram of the apparatus according to the first preferred embodiment of the present invention; 
     FIG. 2 illustrates the biasing conditions associated with the apparatus shown in FIG. 1; 
     FIG. 3 is a schematic diagram of the apparatus according to the second preferred embodiment of the present invention; and 
     FIG. 4 illustrates the biasinbg conditions associated with the apparatus shown in FIG. 3. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring to FIG. 1, the apparatus 10 is shown which has a drain, a gate and a source. The apparatus 10 comprises a first transistor Q1 and a second transistor Q2. Both the transistor Q1 and the transistor Q2 are n-channel metal-oxide-semiconductor-field-effect-transistors (MOSFET), and therefore have virtually infinite input resistance and zero offset voltage. The drain of the transistor Q1 is connected to the source of the transistor Q2 through the conductor 12 as well as a conductor 20 electrically connecting the source of the transistor Q1 with the source of the apparatus 10. In addition, the source of the transistor Q1 is connected to the gate of the transistor Q2 through a conductor 14. A conductor 16 is connected to a gate of the transistor Q1 to provide an input voltage to the apparatus 10. Further, a conductor 18 is also connected between the drain of the transistor Q2 through the drain of the apparatus 10 to a biasing source (not shown) to provide means for biasing the drain of the transistor Q2. The remaining parameters of transistors Q1 and the transistor Q2 are chosen according to a set of selection rules which permit optimum performance of the apparatus 10. These rules are as follows: 
     (1) the transistor Q2 is a depletion mode transistor; 
     (2) both the transistor Q1 and the transistor Q2 operate in their saturation region; and 
     (3) under similar bias conditions, the transistor Q2 in common gate operation exhibits a larger drain saturation current than the transistor Q1 in common source operation, i.e., I D1  as a function of V i  [I D1  =β 2  /2(V i  -V T1 ) 2  ] is less than I D2  as a function of V SG2  [I D2  =β 2  /2(V P2  -V SG2 )] with V DD  greater than V P2 , where the variables are defined in the Table at the end of this description. 
     By using these selection rules, an output resistance of the apparatus 10 is greater than if the selection rules are not used. For example, the output resistance of the apparatus 10 may typically be 300 Mohms when the selection rules are used, while the output resistance of similar circuits formed without the use of the selection rules may typically be less than 1 Mohms. Accordingly, the open-loop gain of the apparatus 10 using the selection rules is greater than the open-loop gain if the selection rules are not used. 
     To describe the operation of the selection rules, reference will be made to FIG. 2 which illustrates the biasing conditions associated with the transistor Q1 and the transistor Q2. First consider the case where a variable bias voltage V DD  is applied to the drain of the transistor Q2 while the input voltage V i  is held constant at a voltage less than the threshold voltage V T1  of the transistor Q1. Under these conditions, the transistor Q1 is nonconducting while the transistor Q2 is conducting. As the variable bias voltage V DD  is increased from zero, substantially all of the variable bias voltage V DD  appears as the drain-source voltage V DS1  of the transistor Q1, i.e., V DS1  is approximately equal to V DD . Since the drain-source voltage V DS1  of the transistor Q1 is equal to the gate-source voltage V GS2  of the transistor Q2, the drain-source voltage V DS2  of the transistor Q2 is approximately zero. Note that as the variable bias voltage V DD  increases, the transistor Q2 is driven toward cut-off thereby reducing the current handling capability of the transistor Q2. Under these input bias conditions, the drain current of each of the transistors Q1 and Q2 is approximately zero (i.e., I D1  =I D2  =0). 
     Next consider the case where the input voltage V i  is held constant at a value greater than V T1 . In this case, both the transistor Q1 and the transistor Q2 are conducting. As the variable bias voltage V DD  is increased from zero, the sum of the drain-source voltages of the transistors Q1 and Q2 will equal V DD  : 
     
         V.sub.DS1 +V.sub.DS2 =V.sub.DD                             (1) 
    
     with the voltage division such that the drain current I D1  of the transistor Q1 is equal to the drain current I D2  of the transistor Q2. As the variable bias voltage V DD  is further increased, the transistor Q1 or the transistor Q2 enters saturation depending on whether V DS1  =V DSAT1  occurs before or after the occurrence of V DS2  =V DSAT2  =V P2 . The conditions defined by Equation (1) must hold under all circumstances, and the drain current I D1  of the transistor Q1 must always equal the drain current I D2  of the transistor Q2. 
     Optimum interaction occurs between the transistor Q1 and the transistor Q2 when the transistor Q1 enters saturation before the transistor Q2. This occurs when the threshold voltage V T1  of the transistor Q1 subtracted from the input voltage V i  is greater than the pinch-off voltage V P2  of the transistor Q2. Accordingly, the transistor Q1 enters saturation before the transistor Q2 when: 
     
         (V.sub.i -V.sub.T1)&lt;V.sub.P2                               (2) 
    
     After the transistor Q1 enters saturation, there is only a small change in its drain current I D1  for a large change in its drain-source voltage Δ(V DS1  -V DSAT1 ). Because the output resistance r o1  of the transistor Q1 is equal to the derivative of the drain voltage V DS1  with respect to drain current I D1  while the gate-source voltage V GS1  is held constant, the change in fthe drain current I D1  of the transistor Q1 can be expressed as follows: 
     
         ΔI.sub.D1 =(1/r.sub.o1)Δ(V.sub.DS1 -V.sub.DSAT1) (3) 
    
     Further increases in the variable bias voltage V DD  results in a much smaller increase in the drain current I D2  of the transistor Q2 as the transistor Q2 is also in saturation. The resultant change in the drain current I D2  of the transistor Q2 as a function of the variable bias voltage V DD  can be expressed as: 
     
         ΔI.sub.D2 =(1/r.sub.o2)Δ(V.sub.DD -V.sub.P2)-g.sub.m2 ΔV.sub.SG2                                          (4) 
    
     where g m2  refers to the transconductance of the transistor Q2 at its point of operation. 
     It will be noted that the change in saturation voltage V DSAT1  of the transistor Q1 subtracted from the drain-source voltage of the transistor Q1 is equal to the change in fthe source-gate voltage ΔV SG2  of the transistor Q2. Accordingly, because the change in drain current I D1  is equal to the change in drain current I D2 , Equation (4) may be rewritten as follows: ##EQU1## Since the output resistance r o  of the apparatus 10 may be defined as drain voltage with respect to change in drain current with the gate voltage held constant, the output resistance r o  of the apparatus 10 may be calculated as follows: ##EQU2## 
     Accordingly, the output resistance r o  of the apparatus 10 is substantially greater than the output resistance of either the transistor Q1 or the transistor Q2 individually. Because the output resistance of the apparatus 10 is related to its open-loop gain, the open-loop gain of the apparatus 10 is also increased. For example, in one embodiment, the transconductance g m  approximately equals 300 μmhos at 100 microamps, and r o1  =r o2  =500 K ohms. Using Equation (6), the output resistance r o  of the apparatus 10 is approximately 150 times greater than the output resistances r o1  and r o2  of the transistors Q1 and Q2. 
     The second preferred embodiment of the present invention is shown in FIG. 3. In this embodiment, the apparatus 10 comprises a first transistor Q1 and a second transistor Q2, both of which are metal-oxide-semiconductor-field-effect-transistors (MOSFET). The source of the transistor Q2 is connected to the drain of the transistor Q1 by means of the conductor 112, and the gate of the transistor Q2 is connected to the gate of the transistor Q1 by means of the conductor 114. Further, a conductor 116 is also connected to the gate of the transistor Q1 to provide means for providing input potential to the gate of the transistor Q1. In addition, a conductor 118 is connected between the drain of the transistor Q2 and a biasinfg source (not shown) so as to provide means for biasing the transistor Q2, while a conductor 120 is connected between the source of the transistor Q2 and the source of the apparatus 10. Finally, both the transistor Q1 and the transistor Q2 are enhancement mode n-channel MOSFETs which are generally more commercially available than depletion mode MOSFETs. 
     To optimize performance of the apparatus 10, the transistors Q1 and Q2 are selected according to a set of selection rules. These selection rules are as follows: 
     (1) The drain current I D2  of the transistor Q2 is larger than the drain current I D1  of the transistor Q1 under the same bias conditions. 
     (2) the saturation current I D  of the apparatus 10 is less than I Dmax  where: 
     
         I.sub.D ≦I.sub.Dmax =(β.sup.2 /2)(V.sub.T1 -V.sub.T2).sup.2 (7) 
    
     By applying these selection rules, the output resistance of the apparatus 10 is much grreater than the output resistance of the apparatus 10 designed without the use of the election rules. Accordingly, the open-loop gain of the apparatus 10 is greater when the selection rules are used. Because the transistors Q1 and Q2 are enhancement mode devices, the apparatus of the second preferred embodiment is easier to fabricate than that of the first preferred embodiment. 
     The operation of the apparatus 10 according to the second preferred embodiment of the present invention will be made with reference to the biasing conditions shown in FIG. 4. First consider the case where a variable bias voltage V DD  is applied to the drain of the transistor Q1, while the input voltage V i  is held constant at a value less than the threshold voltage V T1  of the transistor Q1. Under these circumstances, the transistor Q1 is nonconducting while the transistor Q2 may either be conducting or nonconducting depending whether V i  is less than or greater than the threshold voltage V T2  of the transistor Q2. 
     As one of the conditions for optimum interaction of the transistors Q1 and Q2 is that the threshold voltage V T1  of the transistor Q1 be greater than the threshold voltage V T2  of the transistor Q2, we will first consider the case where the transistor Q1 is nonconducting while the transistor Q2 is conducting (i.e., V T2  &lt;V i  &lt;V T1 ). As the variable bias voltage V DD  is increased from zero, practically all of the variable bias voltage V DD  appears as the drain-source voltage V DS1  of the transistor Q1 (i.e., V DS1  approximately equals V DD .) Since the drain-source voltage V DS1  of the transistor Q1 is also the source voltage of the transistor Q2, the drain-source voltage V DS2  of the transistor Q2 is approximately equal to zero. Note that an increase in the source voltage of the transistor Q2 reduces the current handling capability of the transistor Q2. When V DD  reaches the value of 
     
         V.sub.i -V.sub.DD =V.sub.i -V.sub.DS1 =V.sub.T2            (8) 
    
     the transistor Q2 becomes nonconducting and any further increase in variable bias voltage V DD  will be divided between V DS1  and V DS2  so that I D1  =I D2 . 
     Next consider the case where the input voltage V i  is held constant at a value greater than the threshold voltage V T1  of the transistor Q1. In this case, both the transistor Q1 and the transistor Q2 are conducting. As the variable bias voltage V DD  is increased from zero, the sum of the two drain-source voltages will equal V DD  : ##EQU3## with the voltage division such that the drain current I D1  of the transistor Q1 is equal to the drain current I D2  of the transistor Q2. 
     As the variable bias voltage V DD  is increased further, the transistor Q1 or the transistor Q2 enters saturation depending on whether V DS1  =V DSAT1  occurs before or after the occurrence of V DS2  =V DSAT2 . Note that the conditions defined by Equation (9) will hold under all circumstances, and that the drain current I D1  of the transistor Q1 be equal the drain current I D2  of the transistor Q2. 
     Optimum interaction occurs between the transistor Q1 and the transistor Q2 when the transistor Q1 enters saturation before the transistor Q2. A better understanding of what influences the saturation condition can be obtained from reviewing the expression of the drain current I D  of a MOSFET operating in the triode region in common source configuration: 
     
         I.sub.D =β[(V.sub.G -V.sub.T)V.sub.DS -(V.sub.DS.spsb.2 /2)](10) 
    
     Saturation occurs when the drain-source voltage V DS  is equal to the gate voltage V G  less the threshold voltage V T . Since V G  is constant, the condition for saturation to occur is a function of the drain-source voltage V DS . Accordingly, to insure that the transistor Q1 enters saturation before the transistor Q2, the drain-source voltage V DS1  of the transistor Q1 should be much greater than the drain-source voltage V DS2  of the transistor Q2. This condition will be satisfied if the current handling capability of the transistor Q2 is larger than the current handling capability of the transistor Q1. Comparing the drain current I D1  of the transistor Q1 to the drain current I D2  of the transistor Q2, the following can be obtained: 
     
         I.sub.D1 =β.sub.1 [(V.sub.GS1 -V.sub.T1)V.sub.DS1 -(V.sub.DS1.spsb.2 /2)]                                                      (11) 
    
     
         I.sub.D2 =β.sub.2 [(V.sub.GS2 -V.sub.T2)V.sub.DS2 -(V.sub.DS2.spsb.2 /2)]                                                      (12) 
    
     Note that while the gate-source voltage V GS1  of the transistor Q1 is equal to the input voltage V i , te gate-source voltage V GS2  of the transistor Q2 will be equal to the input voltage V i  less the drain-source voltage V DS1  of the transistor Q2. Under all circumstances, the drain current I D1  of the transistor Q1 is equal to the drain current I D2  of the transistor Q2. 
     To satisfy the requirement than the drain-source voltage V DS1  of the transistor Q1 be much greater than the drain-source voltage V DS2  of the transistor Q2, it is required that 
     
         β.sub.2 &gt;β.sub.1                                 (13) 
    
     
         V.sub.T2 &lt;V.sub.T1                                         (14) 
    
     To clarify the conditions set forth in the Equations (13) and (14), it is known that for the transistor Q1: 
     
         V.sub.GS1 -V.sub.T1 =V.sub.i -V.sub.T1                     (15) 
    
     and for the transistor Q2: 
     
         V.sub.GS2 -V.sub.T2 =V.sub.1 -V.sub.DS1 -V.sub.T2          (16) 
    
     For the drain current I D2  of the transistor Q2 to be much greater than the drain current I D1  of the transistor Q1 for giving input voltage V i , the input voltage V i  less the drain-source voltage V DS1  of the transistor Q1 less the threshold voltage V T2  of the transistor Q 2  must be greater than zero. This must be valid for the saturation current I DSAT2  of the transistor Q2 as well as for I DSAT1  of the transistor Q1. Saturation for the transistor Q1 occurs when the drain-source voltage V D1  of the transistor Q1 equals: 
     
         V.sub.DS1 =(V.sub.i -V.sub.T1)=V.sub.DSAT1                 (17) 
    
     When applying Equation (17) to Equation (11), the saturation current I DSAT1  for the transistor Q1 is obtained: 
     
         I.sub.DSAT1 =(β.sub.1 /2)(V.sub.i -V.sub.T1).sup.2    (18) 
    
     Similarly, saturation occurs for the transistor Q2 when 
     
         V.sub.DS2 =(V.sub.GS2 -V.sub.T2)=(V.sub.i -V.sub.DSAT1 -V.sub.T2)=(V.sub.T1 -V.sub.T2)                                                (19) 
    
     When applying Equation (19) to Equation (12), the saturation current I DSAT2  for the transistor Q2 is obtained 
     
         I.sub.DSAT2 =β.sub.2 /2)(V.sub.T1 -V.sub.T2).sup.2    (20) 
    
     Note that I DSAT2  is independent of V i  and therefore Equation (20) defines the maximum drain current I D  of the apparatus 10, which assures optimum interactiobn between the transistor Q1 and the transistor Q2. When the drain current I D  of the apparatus 10 exceeds the maximum drain current I Dmax  of the apparatus 10, there is interaction between the transistor Q1 and the transistor Q2 and increased output resistance can be obtained, but the conditions are not optimized. 
     It should be understood that the invention was described in connection with the particular example thereof. Other modifications will be apparent to those skilled in the art after study of the specification, drawings and following claims. 
     
                       TABLE______________________________________Term          Description______________________________________V.sub.DD      Variable bias voltageV.sub.GS1, V.sub.GS2         Gate-source voltages of transistors         Q1 and Q2 respectivelyV.sub.DS1, V.sub.DS2         Drain-source voltage of transistors         Q1 and Q2 respectivelyV.sub.DSAT1, V.sub.DSAT2         Saturation voltages of transistors Q1         and Q2 respectivelyr.sub.o, r.sub.o1, r.sub.o2         Output resistance of the apparatus,         the transistor Q1 and the transistor         Q2 repectivelyV.sub.T1, V.sub.T2         Threshold voltages for transistors Q1         and Q2 repsectivelyV.sub.P1, V.sub.P2         Pinch-off voltage of transistors Q1         and Q2 respectivelyI, I.sub.D1, I.sub.D2         Drain current of the apparatus, the         transistor Q1 and the transistor Q2         respectivelyI.sub.Dmax    Maximum drain current of the         apparatusβ.sub.1, β.sub.2          ##STR1##         of the transistors Q1 and Q2         respectively______________________________________