General-purpose temperature compensating current master-bias circuit

[0002] 1. Field of the Invention

[0003] This invention relates to electronic circuits and systems. More particularly, this invention relates to circuits that generate biasing currents for circuits. This invention, especially, relates to circuits that generate biasing currents that provide variations in these biasing currents to compensate for functional circuit variations due to changes in operating temperature of the functional circuits.

[0004] 2. Description of Related Art

[0005] Presently designed analog circuits generally employ current biasing rather than voltage biasing. Current biasing, firstly, allows the operating points of the transistors to be relatively independent of the fabrication process parameters. Secondly, current biasing is less prone to noise pickup. Thirdly, the temperature coefficient of the biasing current can be easily altered to provide temperature compensation to some of the small signal parameters, particularly, transconductance (g_m) of transistors. For the purpose of current biasing, a current master-bias circuit is usually employed. However, the slope of the temperature characteristic of the bias current from the master-bias circuit might have to be different for different circuits and even for the same circuit using different fabrication processes, if reasonably precise temperature compensation is required. Therefore, a master-bias current circuit must be able be easily adaptable to provide different characteristics for the bias current.

[0006] A Proportional To Absolute Temperature (PTAT) current generator as shown in FIG. 1 is very widely used as a temperature compensated current master-bias circuit. The NPN bipolar transistors Q1 and Q2, resistor R1, and an active current mirror circuit CM1 form the PTAT current generator. The current mirror circuit CM1 forces the collector currents of transistors Q1 and Q2 to be equal which is shown as I_C1and I_C2. If the small base current of Q1 is ignored, it can be shown that the collector currents I_C1and I_C2of transistors Q1 and Q2 is determined by the equation: $\begin{array}{cc}{I}_{\mathrm{C1}}=I_{\mathrm{C2}}=\frac{V_{{\mathrm{be}}_{\mathrm{Q2}}}-V_{{\mathrm{be}}_{\mathrm{Q1}}}}{R_1}& \mathrm{Eq}.1\end{array}$

[0007] where:

[0008] V_beQ1and V_beQ2are the voltages developed between the base and emitter respectively of the transistors Q1 and Q2.

[0009] R₁is the resistance of the resistor R1.

[0010] It is known that the base emitter voltages V_beQ2& V_beQ1of the transistors Q1 and Q2 are determined by the equation: $\begin{array}{cc}{V}_{\mathrm{be}}=V_T\ln \left(\frac{I_C}{J_{S}A}\right)& \mathrm{Eq}.2\end{array}$

[0011] where:

[0012] V_Tis a thermal voltage given by the equation: $\begin{array}{cc}{V}_T=\frac{\mathrm{kT}}{q}& \mathrm{Eq}.3\end{array}$

[0013] where:

[0014] k is Boltzmann's constant,

[0015] T is the operating temperature of the transistor generally in degrees Kelvin, and

[0016] q is the electrical charge of an electron.

[0017] I_Cis the collector current of an NPN transistor.

[0018] J_Sis the saturation current density per unit area.

[0019] A is the emitter area.

[0020] By substituting Eq. 2 and Eq. 3 into Eq. 1, it can be shown that the collector currents I_C1and I_C2of transistors Q1 and Q2 are equal to: $\begin{array}{cc}\begin{array}{c}{I}_{\mathrm{C1}}=I_{\mathrm{C2}}=\frac{V_T}{R_1}\ln \left(\frac{I_{\mathrm{C2}}}{J_S{A}_2}\right)-\ln \left(\frac{I_{\mathrm{C1}}}{J_S{A}_1}\right)\\ =\frac{V_T}{R_1}\ln \left(\frac{A_2}{A_1}\right)={\mathrm{AV}}_T\end{array}& \mathrm{Eq}.4\end{array}$

[0021] If the current mirror CM1 is designed such that the MOS transistors M1, M2, and M3 are of equal sizes, then the PTAT current I_PTATis equal to collector currents I_C1and I_C2and is given by the equation:

[0022] I_PTAT=AV_T  Eq. 5

[0023] where: $A=\frac{1}{R_1}\ln \left(\frac{A_2}{A_1}\right)$

[0024] and is the constant simplified from the terms of Eq. 4.

[0025] V_Tis the thermal voltage of Eq. 3.

[0026] FIG. 2 shows the temperature behavior of the PTAT current I_PTATversus temperature. The constant $A\frac{k}{q}$

[0027] is the slope of the line. This kind of linear characteristic is usually very effective for providing temperature compensation for Bipolar transistors.

[0028] The transconductance g_mbipfor a bipolar transistor is given by: $\begin{array}{cc}{g}_{\mathrm{mbip}}=\frac{I_C}{V_T}& \mathrm{Eq}.6\end{array}$

[0029] where,

[0030] I_Cis the collector current.

[0031] If a bipolar transistor is biased by a PTAT current I_PTAT, the PTAT current I_PTATfound in Eq. 5 is substituted for the collector current I_Cin Eq. 6, the transconductance g_mbipof the bipolar transistor becomes:

[0032] g_mbip=A.  Eq. 7

[0033] Thus the PTAT current generator effectively forces the transconductance of the bipolar transistor to be constant over temperature.

[0034] Conversely, for MOS transistors in strong-inversion, the PTAT current generator does not provide an effective temperature compensation. The transconductance g_mMosof a MOS transistor is given by the equation: $\begin{array}{cc}{g}_{\mathrm{mMOS}}=\sqrt{2I_D\mu C_{\mathrm{OX}}\frac{W}{L}}& \mathrm{Eq}.8\end{array}$

[0035] where:

[0036] I_Dis the drain current of the MOS transistor.

[0037] C_OXis the gate oxide capacitance per unit area of the MOS transistor.

[0038] W/L the aspect ratio of the MOS transistor

[0039] μ the carrier mobility given by the equation:

[0040] μ=BT^−m

[0041] where:

[0042] B is a constant.

[0043] m is a process dependent exponent that has a typical value of 1.5.

[0044] T is temperature in degrees Kelvin.

[0045] If a MOS transistor is biased by a PTAT current I_PTAT, the PTAT current I_PTATfound in Eq. 5 is substituted for the drain current I_Din Eq. 8, the transconductance g_mMosof the MOS transistor is found by the equation: $\begin{array}{cc}{g}_{\mathrm{mMOS}}=\sqrt{\frac{2{\mathrm{kABWC}}_{\mathrm{OX}}}{\mathrm{qL}}}{T}^{\frac{1-m}{2}}& \mathrm{Eq}.9\end{array}$

[0046] It is known in the art the process dependent exponent m is not easily controllable and is almost never has a magnitude of 1. Thus it becomes obvious from Eq. 9 that the transconductance g_mMoshas a level of temperature dependence even if biased with a PTAT current I_PTAT

[0047] U.S. Pat. No. 6,157,245 (Rincon-Mora) describes a curvature corrected bandgap reference voltage circuit, the output voltage that is substantially linear and independent of the operating temperature of the circuit. The circuit includes a voltage divider network comprised of a first resistor and a second resistor connected in series. A first compensating circuit provides a first, linear, operating temperature-dependent current, and a second compensating circuit provides a second, logarithmic, operating temperature-dependent current. The first current is supplied to the first resistor of the voltage divider network, while the second current is supplied to the second resistor of the voltage divider network.

[0048] U.S. Pat. No. 5,952,873 (Rincon-Mora) illustrates a low voltage, current-mode, piecewise-linear curvature corrected bandgap reference circuit. The bandgap circuit includes a first current source supplying a current proportional to a base-emitter voltage, a second current source supplying a current proportional to absolute temperature, and a third current source supplying a non-linear current. Three resistors are coupled in series between a first node and ground. The first current source is coupled to the first node. The second current source is coupled to a second node between the first and second resistors. The third current source is coupled to a third node between the second and third resistors. An output coupled to the first node supplies a reference voltage.

[0049] U.S. Pat. No. 5,883,507 (Yin) describes a low power temperature compensated, current source. The current source creates a first reference current and a temperature compensating voltage-controlling circuit generates a temperature compensated voltage control signal during temperature variations. A bias controlling circuit is connected to the current generating circuit and the temperature compensating voltage control circuit to bias the temperature compensating voltage control circuit. A current output controlling circuit is connected to the current generating circuit and the temperature compensating voltage controlling circuit for controlling a second temperature compensated reference current to generate a high output source current even during low temperature conditions.

[0050] U.S. Pat. No. 5,796,244 (Chen et al.) teaches a voltage reference circuit that will remain constant and independent of changes in the operating temperature that is correlated to the bandgap voltage of silicon is described. The voltage reference circuit will be incorporated within an integrated circuit and will minimize currents into the substrate. The bandgap voltage reference circuit has a bandgap voltage referenced generator that will generate a first referencing voltage having a first temperature coefficient, and a compensating voltage generator that will generate a second referencing voltage having a second temperature coefficient. The second temperature coefficient is approximately equal to and has an opposite sign to the first temperature coefficient. A voltage summing circuit will sum the first referencing voltage and the second referencing voltage to create the temperature independent voltage. A voltage biasing circuit will couple a bias voltage to the bandgap voltage referenced generating means to bias the bandgap voltage referenced generator to generate the first referencing voltage.

[0051] U.S. Pat. No. 6,191,646 (Shin) teaches a temperature-compensated high precision current source, which provides a constant current regardless of temperature change. The temperature-compensated high precision current source has a control circuit connected to a voltage supply for producing control signal. A first current generating circuit generates a first current, which is proportional to absolute temperature in response to the signals from the control circuit. A first current transferring circuit transfers the first current to a common node. A second current generating circuit generates a second current, which is inversely proportional to absolute temperature in response to the signals from the control circuit. A second current transferring circuit transfers the second current to the common node. The common node adds the first and second currents to generate a third current that is compensated for a current variation caused by the temperature variation at the first and second current generating circuits. An output circuit is connected to the common node for receiving the third current from the common node and generating a constant output current.

[0052] An object of this invention is to provide a circuit that generates a master biasing current that has a unique variation with changes in temperature.

[0053] Another object of this invention is to provide a circuit that generates a master biasing current and biasing currents mirrored from the master biasing current such that the master biasing current and the mirrored biasing currents have unique variation with changes in temperature.

[0054] To accomplish at least one of these as well as other objects, a temperature compensating biasing circuit is constructed by first determining a piecewise function substantially describing a required bias current with respect to temperature. Reference signals are created such that each reference signal describes an amount of a contributing current of a plurality of contributing currents. The selected contributing currents, when summed together, generate the master biasing current. The biasing current generator is further constructed to create a thermal signal, such that the magnitude of the thermal signal indicates a temperature of the functional circuit to which the biasing currents are supplied. Each of the reference signals is compared to the thermal signal. The biasing current generator then identifies which of the contributing currents or portions of the contributing currents are being included to generate the master biasing current. The identified contributing currents and the portions of the contributing currents are then summed to form the master biasing current.

[0055] To accomplish the function as above described, the temperature compensating bias current generator has a temperature-to-current converter to provide a thermal signal indicating a temperature value of current and a current function generator in communication with the temperature-to-current converter to multiply the thermal signal by a bias function having the unique temperature characteristics to create the master biasing current. The temperature-to-current converter has a temperature independent current source, a proportional-to-absolute-temperature current source, and a current difference circuit. The temperature independent current source provides a first current that does not fluctuate with a change in temperature. The proportional-to-absolute-temperature current source provides a second current that varies by a known function (generally linear) with temperature. The current difference circuit is connected to the temperature independent current source and the proportional-to-absolute-temperature current source to receive the first and second currents and from the first and second currents generates the thermal signal. The thermal signal is indicative of a difference between the first and second currents, which a current measure of the temperature.

[0056] The current function generator is in communication with the temperature-to-current converter to receive the thermal signal. The thermal signal is compared with the reference signals to determine which of the contributing currents or portions of the contributing currents indicated by the reference signals are to be added to form the master biasing current. The reference signals are generated by a bandgap voltage generator and are chosen to determine the bias function.

[0057] The master biasing current may be used as the reference current for a plurality of mirrored current sources that provide a plurality of bias currents that have the temperature compensation bias function as determined by the master biasing current.

[0058] The current difference circuit includes a current subtractor circuit. The current subtractor circuit is in communication with the temperature independent current source and the proportional-to-absolute-temperature current source to receive the first and second currents and to subtract the first and second to generate a thermal current. A signal converter is connected to the current subtractor to receive the thermal current and convert the thermal current to the thermal signal.

[0059] The current function generator comprises a current multiplier in communication with the temperature-to-current converter to receive the thermal signal, compare the thermal signal with the reference signals to determine a contributing currents indicated by the reference signals to be added to form the master biasing current. The current multiplier is formed of a plurality of current steering circuits, each current steering circuit comparing the thermal current difference signal to one of the plurality of reference signals to selectively steer all or some of one of the contributing currents to an output node. The current steering circuits are all connected to a current summing node to additively combine the selectively steered contributing currents to form the master biasing current.

[0060] Each current steering circuit has a first and second MOS transistor. The first MOS transistor has a gate to receive the thermal signal, and a drain connected to a voltage reference terminal, and the a second MOS transistor has a gate to receive one of the reference signals, and a drain connected to the current summing node to provide some or all of the contributing current. A first current source is in communication with a source of the first MOS transistor to provide some or all a first portion of the contributing current, and a second current source is in communication with a source of the second MOS transistor to provide some or all a second portion of the contributing current. A resistor is connected between the sources of the first and second MOS transistors such that some or all of the first and second portions or the contributing current selectively flow through the first or second MOS transistor.

[0061] The current steering circuit adjusts the contributing current such that, if the thermal signal has a magnitude between a sum and a difference of the reference signal at the gate of the second MOS transistor and a signal developed at the resistor, an amount of the contributing current transferred to the output node is determined by the equation: $I_y=I_1+\frac{V_c-V_{\mathrm{R1}}}{R}$

[0062] where:

[0063] I_yis the amount of the contributing current,

[0064] I₁is a magnitude of the first portion of the contributing current,

[0065] V_Cis the thermal signal,

[0066] V_R1is the reference signal, and

[0067] R is the resistance of the resistor.

[0068] However, each current steering circuit adjusts the current steering current such that, if the thermal signal has a magnitude that is less than the difference of the reference signal at the gate of the second MOS transistor and the signal developed at the resistor, the amount of the contributing current transferred to the output node is zero. Finally each current steering circuit adjusts the contributing current such that, if the thermal signal has a magnitude greater than the sum of the reference signal at the gate of the second MOS transistor and the signal developed at the resistor, the amount of the contributing current transferred to the output node is a sum of the first and second portions of the contributing current.

[0069] FIG. 1 is a schematic diagram of a proportional-to-absolute-temperature current generator of the prior art.

[0070] FIG. 2 is a plot of the output current of the proportional-to-absolute-temperature current generator of FIG. 1 versus temperature.

[0071] FIG. 3 is a functional block diagram of a master biasing current generator of this invention.

[0072] FIG. 4 is a plot of a segment of the thermal signal of the master biasing current generator of this invention versus temperature.

[0073] FIG. 5 is schematic diagram of the master biasing current generator of this invention.

[0074] FIG. 6 is schematic diagram of a current steering circuit of this invention.

[0075] FIG. 7 is a plot of the first and second portions of the contributing currents and the total contributing current provided by the current steering circuit of FIG. 6 as a function of the thermal signal of this invention.

[0076] FIG. 8 is a plot of the master biasing current as a function of the thermal signal of this invention.

[0077] A temperature compensating biasing circuit of this invention provides the biasing currents to functional circuits to compensate for variation in the operating parameters of the functional circuits. It is known in the art that adjusting the biasing currents can compensate temperature effects on functional circuits. The temperature compensating biasing circuit functions by first generating a thermal signal indicative of the operating temperature of the circuitry. The thermal signal is compared to multiple reference signals. Some or all of a group of contributing currents are summed to form the master biasing current. The master biasing current is constructed by first determining a piecewise function substantially describing a required bias current with respect to temperature. The reference signals are created such that each reference signal describes an amount of a contributing current of a plurality of contributing currents. The selected contributing currents, when summed together, generate the master biasing current. The biasing current generator then identifies which of the contributing currents or portions of said contributing currents are to be included to generate the master biasing current. The identified contributing currents and the portions of the contributing currents are then summed to form the master biasing current.

[0078] Refer now to FIG. 3 for a detailed description of temperature biasing circuit of this invention. The temperature-to-current converter TCC has a reference current generator I_REFthat produces a temperature independent current I_RXand a current source I_PTATthat produces proportional-to-temperature current. The temperature independent current I_RXand the proportional-to-temperature current I_PTATare inputs to the subtractor S₁. The subtractor S₁subtractively combines the temperature independent current I_RXand the proportional-to-temperature current I_PTATto form the output of the subtractor S₁that is a thermal control current I_C(t). The output of the subtractor S₁is the input to the current-to-voltage converter IVC. The current-to-voltage converter IVC generates a thermal signal V_C(t) at its output. The thermal signal V_C(t) in this embodiment is a voltage that is an input to a current function generator IGEN. Refer to FIG. 4 for a discussion of the function of the thermal signal V_C(t) versus temperature. In this instance, the thermal signal V_C(t) has a linear function of the equation:

[0079] V_C(t)=C+D(t−t_min)

[0080] where:

[0081] C is the value of the of the thermal signal V_C(t) at the minimum temperature t_min.

[0082] D is the slope of the function.

[0083] t is the present temperature of the circuit.

[0084] The current function generator IGEN has a bandgap referenced voltage generator V_REFthat generates the multiple reference signals V_R1, V_R1, V_R2, . . . , V_Rnthat are used to describe temperature characteristics of the desired function of the master biasing generator output current I_OUT. The multiple reference signals V_R1, V_R1, V_R2, . . . , V_Rnare the inputs with the thermal signal V_C(t) to the nonlinear-current-multiplier circuit NLCM. The contributing reference current IR is transferred from the reference current source I_REFto the nonlinear-current-multiplier circuit NLCM. The contributing reference current I_Ris mirrored to form the individual reference currents that are summed to create the master biasing generator output current I_OUT.

[0085] The thermal signal V_C(t) is compared to each of the individual multiple reference signals V_R1, V_R1, V_R2, . . . , V_Rn. Based on this comparison some or all of portions of the individual reference currents are generated and then summed to create the master biasing generator output current I_OUT.

[0086] The output of the master current generator IGEN is connected to the current mirror circuit IM. The current mirror circuit IM mirrors the master biasing generator output current I_OUTto generate the biasing currents I_OUT1, I_OUT2, I_OUT3, and I_OUTi. The biasing currents I_OUT1, I_OUT2, I_OUT3, and I_OUT1provide biasing currents to functional circuits to compensate for changes in operation of the functional circuits due to changes in temperature.

[0087] A preferred embodiment of the temperature compensated biasing current generation circuit is shown in FIG. 5. Refer now simultaneously FIGS. 3 and 5. The MOS transistors MA0, MB0 and the amplifier A₁form the temperature independent current source I_REF. The transistors MA0 is configured as a current source. The transistors MB0, MC0, ML1, MR1, ML2, MR2, . . . , MLn, MRn are current mirrors. The current source reference current I_Ris a temperature independent current that is determined by the MOS transistor MD0, the amplifier A₁and the resistor R_X, and the reference voltage VR0. The reference voltage V_R0is referenced to the bandgap of the semiconductor. The amplifier A₁ensures that the reference voltage V_R0is maintained across the resistor R_X. The current I_Rthrough the resistor R_Xand MOS transistors MA0 and MD0 is forced to be: $I_R=\frac{V_{\mathrm{R0}}}{R_X}$

[0088] Neglecting the temperature variations of the resistor R_X, the current I_Ris independent of temperature variations. The currents I_Rx, I₀, I₁, . . . , I_nare mirrored from the current I_Rand are therefore, proportional to the current I_R.

[0089] The temperature independent reference current I_RXis transferred from the drain of the MOS transistor MB0 and is mirrored from the reference current I_R. The temperature independent reference current I_RXis transferred to the subtracting node S1. The proportional-to-absolute-temperature current source I_PTATis connected to the subtracting node S1 and is arranged such that the thermal current I_C(t) is the difference between the temperature independent reference current I_RXand the proportional-to-absolute-temperature current source I_PTAT.

[0090] The amplifier A₂and the resistor R_yform the current-to-voltage converter IVC. The resistor R_yis connected between the inverting input and the output of the amplifier A₂. The thermal current I_C(t) is forced through the resistor R_Yand the output of the amplifier A₂is becomes the voltage of the thermal signal V_C(t). The thermal signal V_C(t) is applied to the current steering circuits CS1, CS2, and CSn.

[0091] Refer now to FIG. 6 for a discussion of the structure and function of the current steering circuits CS1, CS2, and CSn. The thermal signal V_C(t) is applied to the gate of the first MOS transistor MAi. The drain of the first MOS transistor MAi is connected to the power supply ground return. The gate of the second MOS transistor MBi is connected to one of the reference signals V_Riand the drain is connected to the output terminal that sources the contributing current I_Yi. The resistor R_iis connected between the sources of the MOS transistors MAi and MBi. The first current source I_iLis connected between the power supply voltage source V_DDand the source of the first transistor MAi and the second current source I_iRis connected between the power supply voltage source V_DDand the source of the second transistor MBi. The magnitude of each of the currents provided by the current sources I_iLand I_iRare equal to the current I_ithrough the resistor R_i.

[0092] The current steering circuit adjusts the contributing current I_Yisuch that, if the thermal signal V_C(t) has a magnitude between a sum and a difference of the reference signal V_Riat the gate of the second MOS transistor MB and a signal I_jR_ideveloped at the resistor R_i, an amount of the contributing current I_Ytransferred to the output node is determined by the equation: $\begin{array}{cc}{I}_{\mathrm{yi}}=I_i+\frac{V_c-V_{\mathrm{Ri}}}{R_i}& \mathrm{Eq}.10\end{array}$

[0093] where:

[0094] I_yis the amount of the contributing current,

[0095] I_1Ais a magnitude of the first portion of the contributing current,

[0096] V_Cis the thermal signal,

[0097] V_R1is the reference signal, and

[0098] R₁is the resistance of the resistor R₁.

[0099] As can be shown, the thermal signal V_Cof Equation 10 is:

[0100] V_Ri−I_iR_i<V_C<V_Ri+I_iR_i

[0101] and therefore, the contributing current I_Yibecomes: $\begin{array}{c}{I}_{\mathrm{yi}}=0\\ I_{\mathrm{yi}}=2I_i\end{array}❘\begin{array}{c}{V}_{\mathrm{Ri}}-I_i{R}_i\\ V_{\mathrm{Ri}}+I_i{R}_i\end{array}$

[0102] If the thermal signal V_C(t) has a magnitude that is less than the difference of the reference signal V_Riat the gate of the second MOS transistor and the signal IR_ideveloped at the resistor R_i, the amount of the contributing current I_Ytransferred to the output node is zero. If the thermal signal V_C(t) has a magnitude greater than the sum of the reference signal V_Riat the gate of the second MOS transistor and the signal IR_ideveloped at the resistor, the amount of the contributing current I_Yitransferred to the output node is twice the current I_ithrough the resistor R_i.

[0103] FIG. 7 shows that how a piecewise linear output current characteristic can be obtained by adding two such current steering circuits for instance CS1 and CS2 of FIG. 5 with different values of current sources I₁and I₂and resistors R₁and R₂. As the temperature increase from a minimum temperature T₀, the thermal signal V_C(t) increases from V_C0. The current I_Y1from the current steering circuit CS1 increases from a zero level to the value of 2I₁as determined by Eq. 10. When the thermal signal V_C(t) reaches the value V_C1, the output current I_Y1of the current steering circuit becomes equal to 2I₁and remains at that level regardless of the change of the thermal signal V_C(t). The output current I_Y2from current steering circuit CS2 remains at a zero level for the thermal signal V_C(t) at a value less than V_C1and begins to rise according to the function of Eq. 10 when the thermal signal V_C(t) reaches the value of V_C1. The current I_Y2rises as the temperature rises until the thermal signal V_C(t) reaches the value V_C2. The current I_Y2then equal 2I₂and remains at this level independent of the change in temperature.

[0104] The contributing currents I_Y1and I_Y2are summed at the node S2 to form the current I_OUThaving the function as shown. It is worth mentioning that the output current I_Yiin FIG. 5 does not follow the expressions given exactly. The current saturates less abruptly compared to what is predicted. This effect is also shown in FIG. 7 with the fine dotted traces. However, this results in a smoother overall characteristic because of the overlap of currents from the various current steering circuits.

[0105] Referring back to FIGS. 3 and 5, the output node of each of the current steering circuits CS1, CS2, and CSn is connected to the summing node S2. The current mirror formed by the MOS transistor MCO provides the fundamental contribution current I₀to the summing node S2. The master biasing current I_OUTis the sum of the fundamental contribution current I₀and some or all of the portions created as described in FIG. 6 of the contributing currents I_Y1, I_Y2, . . . , I_Ynas formed at the summing node S₂, as shown in the equation: $I_{\mathrm{out}}\left(V_c\right)=I_0+\sum _{i=1}^n{I}_i\left(V_c\right)$

[0106] where: $\begin{array}{cc}{I}_i\left(V_c\right)=I_i+\frac{V_c-V_{\mathrm{Ri}}}{R_i}& ❘V_{c\left(i-1\right)}\le V_c\le V_{\mathrm{ci}}\\ =0& ❘V_c<V_{c\left(i-1\right)}\\ =2I_i& ❘V_c>V_{\mathrm{ci}}\end{array}$  V_Ci−V_C(i−1)=2I_iR_i

[0107] The master biasing current I_OUTis the control current input to the current mirror IM. The MOS transistors M_O0, M_O1, M_O2, M_O3, . . . M_Oiare configured to form the current mirror IM. The ratios of the device structures of the transistors M_O0, M_O1, M_O2, M_O3, . . . M_Oidetermine the biasing currents I_OUT1, I_OUT2, I_OUT3, and I_OUTi, which are proportional to the master biasing current and maintain the temperature relationship established by the nonlinear current multiplier NLCM.

[0108] The bandgap referenced voltage generator V_REFgenerates the reference signals V_R0, V_R1, V_R2, . . . , V_Rn−1, V_Rnthat determine in a piecewise fashion of the function of the master biasing current I_OUT. The bandgap referenced voltage generator V_REFin the preferred embodiment is referenced to a bandgap voltage source V_BG. The bandgap voltage source is the non-inverting input to the amplifier A₃. The amplifier A₃is a configured as a voltage buffer circuit to isolate the bandgap voltage source V_BGfrom the loading of the biasing current generator of this invention. The resistors R_D0, R_D1, R_D2, . . . , R_Dn−1, R_Dnare serially connected to form a voltage divider. The reference signals V_R0, V_R1, V_R2, . . . , V_Rn−1, V_Rnare created at the junction of each pair of the serially connected resistors R_D0, R_D1, R_D2, . . . R_Dn−1, R_Dn. The values of the resistors R_D0, R_D1, R_D2, . . . , R_Dn−1, R_Dnare chosen such that the reference signals V_R0, V_R1, V_R2, . . . , V_Rn−1, V_Rnare determined by the equation: $V_{\mathrm{Ri}}=\frac{V_{c\left(i-1\right)}+V_{\mathrm{ci}}}{2}$

[0109] for

[0110] i=1 to n

[0111] and

[0112] V_C0=V_R0

[0113] where:

[0114] V_C0is the thermal signal representing the minimum temperature of the range of temperatures for which the temperature compensating bias generating circuit is to provide compensation.

[0115] V_R0is the magnitude of the lowest reference signal of the reference signals V_R0, V_R1, V_R2, . . . , V_Rn−1, V_Rnformed by the voltage divider of the reference signal generator V_REF.

[0116] FIG. 8 illustrates the master biasing current I_OUTof a temperature compensating bias current generator of this invention versus the thermal signal V_C(t). The plot of FIG. 8 is used to explain the method to construct the master biasing current I_OUT. The symbolic representation of the effects of temperature on the operating parameters of the functional circuit are described. The thermal signal V_C(t) is substituted for the temperature and the reference signals V_Riare determined as piece-wise functions over the range of the thermal signal V_C(t) to be used. In FIG. 8, the temperature compensating biasing current generator is being designed to have four piece-wise regions A, B, C, and D to describe the master biasing current I_OUT. This means that there are four current steering circuits CSn (where n=4) as shown n FIG. 5. The portions I₁, I₂, I₃, and I₄of the contributing current I_Yiand the resistors R₁, R₂, R₃, and R₄, are selected to determine the slope function of the each of piece-wise regions A, B, C, and D. For temperatures less than a minimum value that yields a thermal signal V_C0, the output current is set to a fundamental contribution current I₀.

[0117] The thermal signal V_C(t) is then compared to each of the reference signals V_R1, V_R2, V_R3, and V_R4. When the thermal signal V_C(t) reaches the value of the reference signal V_R1less the signal I₁R₁developed across the resistor R₁, the master biasing current becomes the value of the contributing current I_Y1as determined by Eq. 10. This is as shown in Region A. Upon reaching the value of the reference signal V_R1summed with the signal I₁R₁developed across the resistor R₁, the contributing current I_Y1becomes fixed at the value 2I₁and the second contributing current I_Y2is as determined by Eq. 10 and is added to the master biasing current I_OUT. This is as shown in Region B. As the temperature increases, the master biasing current I_OUTis adjusted by the addition of the contributing currents I_Y3and I_Y4from the current steering circuits CS3 and CS4 as shown in Regions C and D.

[0118] The piece-wise function of the preferred embodiment of this invention is shown as substantially linear as is evident in FIGS. 7 and 8. However, it is keeping with the intent of this invention that any achievable piece-wise function may be used, thus the voltage reference generator V_REFof FIG. 5 maybe more complex than the voltage divider formed of the serially connected resistors R_D0, R_D1, R_D2, . . . , R_Dn−1, R_Dn.

[0119] While this invention has been particularly shown and described with reference to the preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made without departing from the spirit and scope of the invention.