Monolithic transformer compensated circuit

[0002] This application claims the benefit of the filing data of U.S. Provisional Application No. 60/351,369, filed Jan. 28, 2002.

[0003] A major problem in realizing high performance monolithic wireless transceivers arises because of the low Quality (Q) Factors of on-chip inductors. A great deal of effort has been expended to improve the performance of these devices, including patterned ground shields, micromachining to reduce substrate losses, and the development of sophisticated modeling and design software aimed at optimizing the Q Factor in given applications. However, Q Factors in standard processes are limited to something less than 15 at GHz frequencies, in spite of the best efforts of the industrial and scientific communities. Attempts to replace the passive devices with active (transistor based) equivalents can be somewhat effective, but increased distortion, noise and power consumption make these circuits undesirable in battery-powered high gain applications.

[0004] A monolithic transformer compensated circuit with enhanced quality factor without significantly increasing noise levels is presented in this disclosure. The technique uses a monolithic transformer and a current source driving current into the transformer secondary winding to achieve loss compensation in the transformer primary. An ac current which is proportional to, and in phase with the voltage applied to the primary winding can be used to achieve theoretically perfect loss compensation at a given frequency in the RF (GHz) frequency range. The monolithic transformer is preferably frequency stabilized, for example with a stabilizing capacitance in parallel with the transformer secondary winding or an LC circuit in series with the current source. Examples of circuit applications that are particularly suited to the technique include Voltage Controlled Oscillators (VCO's), Low Noise Amplifiers (LNA's) and Filters. The technique has the added advantage of reducing power consumption in some applications.

[0005] There will now be described preferred embodiments of the invention, for the purpose of illustration only, by reference to the drawings, in which identical reference characters denote like elements, but configured in different configurations in the respective figures, and in which:

[0006] FIG. 1 is an equivalent circuit diagram of a representative lossy inductor;

[0007] FIG. 2ashows a means of compensating losses in the inductor of FIG. 1;

[0008] FIG. 2bis an equivalent circuit for the circuit of FIG. 2a;

[0009] FIGS. 3a, 3band 3cshow a lossy resonant circuit, a perfect lossless circuit and a transformer compensated circuit;

[0010] FIG. 4 shows input current for the circuits of FIGS. 3a, 3band 3c;

[0011] FIG. 4ashows variation of compensated Q factor with error factor γ≠1;

[0012] FIG. 5 shows a single inductor with compensation circuit according to the invention;

[0013] FIG. 6 shows variation of input current with frequency for a resonant circuit with no compensation, compensation with a 14% error factor and perfect compensation;

[0014] FIG. 7 shows variation of input current with frequency for a resonant circuit with a compensation input current of 3 mA;

[0015] FIG. 8ashows a conventional monolithic voltage controlled oscillator and FIG. 8bshows the voltage controlled oscillator of FIG. 8amodified according to the invention to include a compensated monolithic transformer;

[0016] FIG. 9ashows a conventional monolithic low noise amplifier and FIG. 9bshows the low noise amplifier of FIG. 9amodified according to the invention to include a compensated monolithic transformer;

[0017] FIG. 10ashows a conventional monolithic filter and FIG. 10bshows the filter of FIG. 10amodified according to the invention to include a compensated monolithic transformer;

[0018] FIG. 11 shows a monolithic transformer compensated circuit, with a capacitor used as a stabilizing element;

[0019] FIG. 12 shows the stabilized monolithic transformer compensated circuit of FIG. 11 in a conventional resonating circuit; and

[0020] FIG. 13 shows a monolithic transformer compensated circuit, with an LC circuit used as a stabilizing element.

[0021] In the claims, the word “comprising” is used in its inclusive sense and does not exclude other elements being present.

[0022] An equivalent circuit diagram of a lossy inductor is shown in FIG. 1. The governing equations for this circuit are as follows:

[0023] I=V_in/(R_S+sL)

[0024] Q=ωL/R_S

[0025] It is desired that Q be large, which corresponds to a small (ideally zero) value of R_S. In that case,

[0026] I=V_in/sL

[0027] Q=∞

[0028] In practice, it is not possible to achieve a very small value of R_S, because of the resistivity of the metal used to fabricate the inductor. However, a means of compensating the loss using a transformer is shown in FIG. 2a. An equivalent circuit that models the transformer and loss components is shown in FIG. 2b. In the equivalent circuit of FIG. 2b,

[0029] V₁=sM₁₂I_S

[0030] V₂=sM₂₁I_P

[0031] Then we can write

[0032] V_in=I_PR_S+I_PsL_P+I_SsM₁₂.

[0033] In order for the input circuit to be purely inductive, Re(I_PR_S+sM₁₂I_P)=0. In its simplest form, making I_PR_S=−I_SsM₁₂sets the entire loss term to zero, so that I_P=V_in/(sL_P), which corresponds to a lossless inductor of value L_P. This condition can be rearranged to yield the required secondary current $I_S=-\frac{I_P{R}_S}{{\mathrm{sM}}_{12}}=-\frac{V_{\mathrm{in}}{R}_S}{s^2{M}_{12}{L}_P}.$

[0034] For sinusoidal signals s=jω and this becomes $I_S=+\frac{V_{\mathrm{in}}{R}_S}{{\omega }^2{M}_{12}{L}_P},$

[0035] which is a real quantity, and readily achievable in circuit form at RF frequencies. In general, $M=k\sqrt{L_P{L}_S}$

[0036] where k is the coupling factor between the primary and secondary windings, typically 0.7 to 0.9 for monolithic transformers in Silicon. Thus the required secondary current becomes, in the general case, $I_S=\frac{V_{\mathrm{in}}{R}_S}{{\omega }^{2}k{L}_P\sqrt{L_P{L}_S}}.$

[0037] If we make a unity turns ratio transformer with L_S=L_Pthe required current reduces to $I_S=+\frac{V_{\mathrm{in}}{R}_S}{k{\omega }^2{L}_P^2}=\frac{V_{\mathrm{in}}}{k{Q}^2{R}_S}$

[0038] where Q is the quality factor of a coil with winding resistance R_Sand inductance L_P. When this current is forced through the secondary winding, the primary circuit behaves like a lossless inductor of value L_P, with infinite Q factor at the frequency ω. This compensation technique is useful in narrowband applications with a fixed value of I_S, or it can be used in wideband applications if the compensation current is made to vary as 1/ω².

[0039] To illustrate the principle discussed, consider three different resonant circuits as shown in FIGS. 3a, 3band 3c, which show respectively a lossy resonant circuit, a perfect lossless circuit and a transformer compensated circuit.

[0040] The values shown are typical values for a monolithic inductor resonating at approximately 1 GHz. The input currents drawn from the signal source in each case are shown in FIG. 4.

[0041] As can be seen in FIG. 4, the transformer compensated circuit behaves essentially the same as the lossless circuit. Note also that the compensation was chosen to be exactly correct at the resonant frequency only, yet the compensation is clearly effective for a range of frequencies near the resonant frequency, which is a significant advantage in the sense that it is not necessary to use a compensation current that is proportional to ω⁻²in the narrowband case. This can be seen by analyzing the general case with a non-unity coupling factor k, and assuming an error factor γ in the secondary compensating current I_S, ie $I_S=+\gamma \frac{V_{\mathrm{in}}{R}_S}{k{\omega }^2{L}_P^2},$

[0042] where γ can be less than or greater than unity, and is ideally unity. In that case, the impedance of the transformer compensated inductor can be shown to be $Z_{\mathrm{comp}}=\frac{R_S\left(1-\gamma \right)+j\omega L_P\left(1+\frac{R_S^2\gamma }{{\omega }^2{L}_P^2}\right)}{1+\frac{R_S^2{\gamma }^2}{{\omega }^2{L}_P^2}}.$

[0043] When γ=1, the compensated inductor is purely inductive, ie lossless.

[0044] In general the compensated circuit with incorrect compensating current can be likened to a new series connection of a resistor R_Scompand an inductor L_PcompSeries, where, by inspection of the equation for Z_comp, recognizing that $\frac{{\omega }^2{L}_P^2}{R_S^2}=Q^2,$

[0045] we see that $R_{\mathrm{Scomp}}=\frac{R_S\left(1-\gamma \right)}{1+\frac{{\gamma }^2}{Q^2}},\mathrm{and}{L}_{\mathrm{ScompSeries}}\frac{L_P\left(1+\frac{\gamma }{Q^2}\right)}{1+\frac{{\gamma }^2}{Q^2}}.$

[0046] Then for convenience, this series circuit can be represented by an equivalent parallel L_PcomParallel−R_Pcompcircuit, where $\begin{array}{c}{R}_{\mathrm{Pcomp}}=R_{\mathrm{Scomp}}\left(1+Q_{\mathrm{comp}}^2\right),\\ L_{\mathrm{PcompParallel}}=L_{\mathrm{PcompSeries}}\left(1+\frac{1}{Q_{\mathrm{comp}}^2}\right),\mathrm{and}\\ Q_{\mathrm{comp}}=\frac{\omega L_{\mathrm{PcompSeries}}}{R_{\mathrm{Scomp}}}.\end{array}$

[0047] With some manipulation, it can be shown that the parallel loss resistance is $R_{\mathrm{Pcomp}}=R_S\left[\frac{{\left(1-\gamma \right)}^2+{Q^2\left(1+\frac{\gamma }{Q^2}\right)}^2}{\left(1-\gamma \right)\left(1+\frac{{\gamma }^2}{Q^2}\right)}\right]$

[0048] where $Q=\frac{\omega L_S}{R_S},$

[0049] the uncompensated Q-factor of the original transformer primary coil.

[0050] The effects of the compensation are best seen by comparing the compensated R_Pcompwith the uncompensated R_P=R_S(1+Q²). Taking the ratio gives $\frac{R_{\mathrm{Pcomp}}}{R_P}=\frac{{\left(1-\gamma \right)}^2+{Q^2\left(1+\frac{\gamma }{Q^2}\right)}^2}{\left(1+Q^2\right)\left(1-\gamma \right)\left(1+\frac{{\gamma }^2}{Q^2}\right)}.$

[0051] If Q²>>1 this becomes $\frac{R_{\mathrm{Pcomp}}}{R_P}\simeq \frac{1}{\left(1-\gamma \right)}.$

[0052] In this case, when γ=1, R_Pcomp=∞, as required.

[0053] It can also be shown that the compensated parallel equivalent inductance is given by $L_{\mathrm{PcompParallel}}=L_P\frac{\left(1+\frac{\gamma }{Q^2}\right)}{\left(1+\frac{{\gamma }^2}{Q^2}\right)}\left(1+\frac{{\left(1-\gamma \right)}^2}{{Q^2\left(1+\frac{\gamma }{Q^2}\right)}^2}\right)$

[0054] Again, when γ=1, L_{PCompParallel}=L_P, ie the value of the inductance is not affected by the compensation.

[0055] Perhaps the most important result is that the compensated Q-Factor of the primary coil is given by $Q_{\mathrm{comp}}=\frac{\omega L_{\mathrm{PcompSeries}}}{R_{\mathrm{Scomp}}}=\frac{Q}{\left(1-\gamma \right)}\left(1+\frac{\gamma }{Q^2}\right)$

[0056] If the original uncompensated coil Q²>>1, this becomes $Q_{\mathrm{comp}}\simeq \frac{Q}{\left(1-\gamma \right)}.$

[0057] This means that even with a 10% error in γ, the compensated inductor has a Q factor 10 times that of the uncompensated circuit. It is also worth noting that Q can be made negative if γ>1 which allows for other losses to be compensated if they appear in parallel with the transformer primary coil. A typical variation in compensated Q factor with γ is shown below, for the case where the uncompensated Q factor is 8.

[0058] The compensation technique for a single inductor can be realized as shown in FIG. 5. In this realization, the voltage Vin is applied to the coil (Inductance Lp), and simultaneously to the gate of the source follower circuit. The resulting signal current that flows in the drain of the transistor is in phase with the voltage, and the drain of the transistor acts as a current source as required to achieve compensation. The bias voltage Vbias, the value of the resistor R and the geometry of the transistor are chosen to achieve the correct compensation current, resulting in a lossless inductor in the transformer primary leads. There are many ways of using Vin to generate the compensation current, for example by using a bipolar transistor instead of a MOS transistor. In addition, tuning of the current can be achieved by replacing the resistor R with another transistor whose bias voltage can then be changed to change the effective resistance. Note that even when γ is in error, significant improvement is obtained, and in fact it may be desirable to choose γ<1 in order to control the degree of Q enhancement. This consideration applies to all the embodiments described.

[0059] The Q-enhanced inductor can be used in any application where inductors are used, including Resonant Circuits, Voltage Controlled Oscillators, Low Noise Amplifiers and Filters. Some examples are given in the following discussion.

[0060] Now that the compensated inductor is characterized, its behavior in a resonant circuit can be examined. If a resonating capacitor is placed in parallel with the compensated inductor, the impedance of the parallel combination is given by $Z_{\mathrm{in}}=\frac{j\omega L_{\mathrm{PcompParallel}}}{1-{\omega }^2{\mathrm{CL}}_{\mathrm{PcompParallel}}+\frac{j\omega L_{\mathrm{PcompParallel}}}{R_{\mathrm{Pcomp}}}}.$

[0061] When 1−ω²CL_{PcompParallel}=0, the impedance of the resonant circuit is simply R_Pcomp, which becomes very large as γ approaches unity. Significant Q enhancement is still obtained when γ is non-unity. For example, if we choose a numerical example where the correct compensating current is 2.73 mA, and instead we have 2.4 mA, the improvement in resonant impedance of 2.6681/0.3406=7.8 times is still achieved, as shown in FIG. 6, which compares input current to the resonant circuit for the cases where there is no compensation (input current at resonance=2.6681 mA), input current when the compensating current is in error by 14% (input current at resonance=340.6 uA), and input current when the coil is properly compensated (input current at resonance=0). Another example with a current of 3 mA instead of 2.73 mA yields a similar result as shown in FIG. 7.

[0062] The method for improving the quality factor will now be used in three different examples. It should be noted that these examples are for illustration only and does not limit the method's uses.

[0063] Voltage Controlled Oscillators

[0064] An example of an application is shown in FIG. 8a. This is a conventional LC Voltage Controlled Oscillator (VCO) with buffer stages to isolate the LC tank circuits from the load circuits. The LC tank circuits are formed from the components L₂and C₁in parallel, and L₁and C₂in parallel.

[0065] In this circuit, inductors L₁to L₄are individual, with L₁and L₂used in the resonant circuits, and L₃and L₄are load components for the buffer transistors M₄and M₅. Because of the low quality factors of the inductors, fairly large bias currents and large transistors are required in order to realize high enough transconductance so that the circuit will oscillate reliably.

[0066] This can be seen as follows: At resonance, the parallel L-C tank circuits, have an equivalent resistance of R_P=(1+Q²)R_S, where R_Sis the series loss resistance associated with each inductor, and Q was defined previously. The circuit comprising M₁, M₂, L₁, L₂, C₁and C₂realizes two voltage amplifiers connected in a loop. The voltage gain from the gate of M₁to its drain is given by g_mR_P, as is the gain from the gate of M₂to its drain. The loop gain is therefore (g_mR_P)², and this is usually designed to have a value of 3 to 5. Since R_Pis small when the inherent inductor Q factor is small, a large $g_m=\sqrt{\frac{2\mu C_{\mathrm{ox}}W{I}_D}{L}}$

[0067] is required, which in turn requires large width to length ratio and high bias current.

[0068] The circuit can be modified to include the transformer compensation. All that is required is to combine L₁and L₃, and L₂and L₄to form Tx₁and Tx₂respectively, as shown in FIG. 8b(the gates could also be cross-coupled and transformer leads inverted to get the same functionality).

[0069] In this example, resistors R₁and R₂are added and can be properly chosen to provide the correct compensating currents in the transformer secondary windings, according to the methods presented in this patent disclosure, so that the inductances of the primary coils are essentially lossless. This corresponds to large values of R_P, and as a result the bias current and transistor dimensions of M₁, M₂and M₃can be reduced significantly while still maintaining enough loop gain to ensure oscillation.

[0070] Low Noise Amplifiers

[0071] Another RF circuit that commonly requires high quality monolithic inductors is the low noise amplifier (LNA) topology shown in FIG. 9a. The LNA shown is a narrowband amplifier, where V_inand R_sourcerepresent the signal and resistance of the previous stage, the transistors M₁and M₂are connected in a cascode arrangement, inductors L_sand L_gare used to improve the high frequency response of the LNA, and C and L are connected to the drain of M₂in parallel to improve the gain and frequency response of the LNA.

[0072] In order to improve the gain of the circuit, the Q-enhanced inductor can be added in a straightforward manner as shown in FIG. 9bby replacing the inductor L with the transformer, transistor M₃, and the resistor R, connected to the circuit using the method described before.

[0073] Filters

[0074] Filters come in a wide variety of configurations, but all have inductive components embedded. The higher the Q factor, the better the performance of the filter. An example of a coupled resonator structure is shown in FIG. 10a, forming a band pass filter. V_inand R_sourceare the signal and output resistance of the previous stage, R_Lrepresents the resistance of the load, and capacitors C₁through C₇and inductors L₁through L₃are chosen according to common methods used in the field, and determine the characteristics of the band pass filter. The characteristics can also be modified by adding more sections such as the section formed by L₁, C₅, and C₂, and selecting appropriate values by the same methods.

[0075] This structure lends itself very well to the Q enhancement technique, as shown in FIG. 10b, where inductors L₁, L₂, and L₃have been replaced with Tx₁, Tx₂, and Tx₃, respectively. The secondary windings of the transformers are driven by transistors M₁, M₂and M₃and resistors R₁, R₂and R₃, where each are connected using the methods described in this patent disclosure.

[0076] Simulations of the VCO circuit behavior in a sophisticated RF circuit simulator called SPECTRE (part of the mainstream commercial IC design package from Cadence Systems) reveal that the technique works very well, allowing a significant decrease in core bias current while maintaining sufficient loop gain to ensure oscillation. In addition, no increase in phase noise is observed, which is very important in VCO design.

[0077] Stability

[0078] There is a stability issue with the monolithic transformer compensated circuit as described in this patent disclosure. Because the effective loss resistance of the compensated inductor continues to become more negative with increasing frequency at frequencies above the point of zero loss, there will usually be a frequency where the circuit becomes unstable (oscillates) for most input terminations.

[0079] This condition may be avoided, and the circuit behavior is substantially improved overall, by the addition of a capacitor C placed in parallel with the secondary windings of the transformer. A preferred embodiment may then look like FIG. 11.

[0080] The resistor R in the original compensated circuit of FIG. 2ahas been replaced with a second transistor M2 in series with M1, adding the additional benefit of allowing electronic variation of the Q-enhancement with voltage Vcontrol. By varying Vcontrol, the ac current through M1 may be controlled, thus providing tuning of the loss compensation. DC bias to M1 and M2 is provided via Vbias and Vdd as shown, although there are many other ways of providing the bias. Capacitor C is chosen such that the input parameter S11 never leaves the unit circle of the Smith Chart, therefore ensuring stability.

[0081] The analytic small-signal expression for the input impedance to the circuit as shown in FIG. 11 is given by $Z_{\mathrm{in}}=\frac{R_s\left(1-\frac{2{\omega }^2}{{\omega }_{\mathrm{res}}^2}\right)+s\left(L_s+{\mathrm{CR}}_s^2-{\omega }^2{L}_s^{2}C\left(1-k^2\right)\right)}{\left(1-\frac{{\omega }^2}{{\omega }_{\mathrm{res}}^2}\right)+s\left({\mathrm{CR}}_s-\frac{g_m{L}_{s}k}{1+g_m{R}_c}\right)},$

[0082] where ${\omega }_{\mathrm{res}}=1/\sqrt{L_{S}C},R_S$

[0083] is the transformer equivalent series loss resistance (assumed to be the same for the primary and secondary circuits), L_Sis the equivalent series inductance of each of the primary and secondary windings,R_Cis the drain-source resistance of transistor M2 in FIG. 11, k is the transformer coupling coefficient, and g_mis the small-signal transconductance of transistor M1 in FIG. 11.

[0084] The entire compensated inductor circuit can then be resonated with a capacitor Cp in order to achieve the desired high Q-factor tuned circuit behavior that is used in most RF circuits, as shown in FIG. 12.

[0085] The small-signal input impedance to the circuit in this case is given by $Z_{\mathrm{in}}=\frac{\left[R_s\left(1-\frac{2{\omega }^2}{{\omega }_{\mathrm{res}}^2}\right)+{\mathrm{sL}}_s\left(1+{\omega }_{\mathrm{res}}^2{C}^2{R}_s^2-\frac{{\omega }^2}{{\omega }_{\mathrm{res}}^2}\left(1-k^2\right)\right)\right]}{\left[1-\frac{{\omega }^2}{{\omega }_{\mathrm{res}}^2}\left(1+\frac{C_p}{C}\right)-{\omega }^2{\mathrm{CC}}_p{R}_s^2+\frac{{\omega }^4}{{\omega }_{\mathrm{res}}^4}\frac{C_p}{C}\left(1-k^2\right)\right]+s\left[\left(C+C_p\right)R_s-\frac{2C_p{R}_s{\omega }^2}{{\omega }_{\mathrm{res}}^2}-\frac{g_m{L}_{s}k}{1+g_m{R}_c}\right]}$

[0086] This circuit exhibits a resonant peak with controllable Q-factor by varying g_mor R_C, or alternatively by varying C.

[0087] The behavior of S11 with frequency for a range of values of C can be analyzed using a conventional Smith Chart, and using reasonable values assigned to the other components and the constants set forward in the immediately preceding equations. A value of C can be chosen (as for example, 9 pF) so that the circuit resonates with infinite Q as the curve crosses the real axis, and then remains inside the circle for all higher frequencies. A value of C for a given circuit may be obtained analytically, or through adjustment of parameters in a simulator. Another way to stabilize the circuit is to use a parallel L-C tuned circuit with a low Q inductor placed in the circuit instead of or in series with the control transistor M1.

[0088] A means to prevent oscillation in the Q-enhanced inductor circuit is shown in FIG. 13. In this case, instead of resonating the secondary transformer winding with a capacitor, a frequency selective LC circuit formed of L1, Rs1 and C1, is placed in series with the source lead of the control transistor M2. Other ways of providing a bandpass filter on the ac current source may be used. This circuit reduces the compensation current at frequencies above the primary resonant frequency, thereby stabilizing the circuit. This technique has the advantage of allowing higher resonant frequencies in the primary circuit with smaller component values, and it does not significantly alter the resonant frequency of the primary L-C circuit compared to the unstabilized circuit. The other stabilization technique using the capacitor C reduces the resonant frequency considerably. In addition, the L1 inductor is quite small and can be quite lossy and is easy to fabricate on chip.

[0089] Immaterial modifications may be made to the circuit described here without departing from the invention.