Design of the 40-MHz Double Differential-Pair Cmos OTA with -60db IM3

Design of the 40-MHz Double Differential-Pair Cmos OTA with -60db IM3

Design of the 40-MHz Double Differential-Pair Cmos OTA with -60db IM3

Yellaboina Venkateswarlu PG Student

Department of Electronics and Communication Engineering, Sree Nidhi Institute of Science and Technology, Hyderabad.

AbstractA configuration of a linearized operational transcon- ductance amplifier (OTA) for low-voltage and high-frequency applications is proposed. By using double pseudo differential pairs and the source-degeneration structure under nano-scale CMOS technology, the nonlinearity caused by short channel effect from a small feature size can be minimized. A robust common-mode control system is designed for input and output common-mode stability and thus reduces distortion caused b y common-mode voltage variation. Tuning ability can be achieved by using MOS transistors in the linear region. The linearity of the OTA is about

60-dB third-order inter-modulation (IM3) distortion for up to 0.9 pp at 40 MHz. This OTA was fabricated by the TSMC 180-nm deep n-well CMOS process. It occupies a small area of

1. 10 3 mm2 and the power consumption is 9.5 mW under a 1.5-V supply voltage.

   Index TermsOperational transconductance amplifier (OTA), pseudodifferential structure, short channel effect, source degeneration.

   1. INTRODUCTION

      HE operational transconductance amplifier (OTA) is one of the most important building blocks in analog and mixed-

      mode circuits, including multipliers [1], [2], continuous-time

      – filters [3], [4], voltage-controlled oscillators (VCOs) [5], and continuous-time sigma-delta modulators [6]. Its main idea is to convert the input voltage into the output current with a linear transformation factor. The active device is used for re- placing passive devices owing to power and area consideration with the tradeoff of linearity. However, as the feature size of CMOS technology scales down with power supply voltage, the dynamic range, bandwidth, and power consumption will be limited by the linearity performance. A variety of lin- earization techniques have been reported in recent years [7]. Most of them exploit the ideal square-law behavior of the MOS transistor in the saturation region to obtain high-linearity conversion. Unfortunately, this concept is not quite suitable for small feature sizes of MOS transistors due to the in- fluence of second-order effects like velocity saturation and mobility reduction

      The use of multiple-input floating-gate (MIFG) MOS tran- sistors was also presented recently [8], [9]. The natural attenu-

      ation could be obtained from the designed capacitor ratio. The MIFG circuit would act as a voltage divider and thus result in a large linear input swing range.

      In this paper, we present a high-linearity and high-speed

      OTA. It makes use of two input transistor pairs with their source terminals connecting to resistor loads and the drain terminals cross-coupled to each other. In the approach, high linearity can be achieved by choosing different values of loading resistors. The model of the short channel effect and the nonlinearity analysis of CMOS transistors are described in Section II, and the proposed OTA implementation is pre- sented in Section III. The analysis of non-ideal effects such as mismatch and noise performance of the proposed circuit are discussed in Section IV. Section V shows the measured perfor- mance of fabricated implementation. Finally, conclusions are drawn in Section VI.

   2. NON LINEARITY ANALYSIS OF SATURATED MOS TRANSISTORS

      1. Linearized Characteristic

         The relationship of the voltage-to-current conversion could be described as , where and are the input voltage and the output current, respectively. The ideal assump- tion of the linearized transformation is , where is a constant within the applied input voltage range. Unfortu-nately, the conversion is not possible to be perfectly linear in real circuit implementation, and the conversion can be inves- tigated by a Taylor series expansion. If the differential structure is applied with well-matched implementations, which means the even-order terms can be cancelled out, the current conversion can be expressed by

         (1)

         where the coefficients are determined from the circuit im- plementation. If the nonlinear factor is suppressed, that is, the parameters are minimized, the conversion would be close to a linear function, as demanded.

         Fig. 2. Nonlinearity cancellation using double pseudodifferential pairs with de- generation resistors.

         Fig. 1. Pseudodifferential circuit by taking short-channel effects into consider- ation.

      2. Saturated MOS Transistor Under Nano-Scale CMOS Technology

         Linear conversion is usually developed based on the basic square-law behavior of the MOS transistor in the satura- tion region [1] as

         source-degenerated resistors are added up to simplify the ex- pression. Assume that transistors M1M4 are operated in the saturation region and that and are the input differential signals, which would be composed of common-mode and dif- ferential-mode voltages

         (2)

         where , and are the width and length of the device, respectively, is the oxide capacitance per unit channel area, is the low-field mobility, and is the nMOS threshold voltage. However, this condition only holds for the large length of MOS transistors. As the device size is scaled

         (4)

         where is the input common-mode voltage and is the input differential-mode voltage. Then, the output current of each transistor could be given by

         down towards nano-scale CMOS technology, the short-channel effect occurs due to the transversal and longitudinal electric

         fields. Thus, with the enhancement of speed and area for small device length, the linearity of conversion based on the ideal square-law equation becomes deteriorated. Fig. 1(a) shows the circuit of the pseudodifferential input pair [12]. If the length of the MOS transistors is chosen to be the minimum feature size

         under nano-scale CMOS technology, the output drain current can be modeled by

         (5)

         (3)

         where is the mobility reduction coefficient. From the equation shown above, the mobility reduction coefficient can be mod- eled by a resistor connected to the source terminal of an ideal MOS transistor, as shown in Fig. 1(b). The value of the equivalent resistor is equal to . Moreover, the linearity per- formance degrades for larger . This is confirmed by the results presented in [13], where tunable resistors are introduced in the source terminals of the pseudodifferential pair for the use of transconductance tuning ability with the expense of additional distortion. In this paper, in order to resist the nonlinearity which occurs by the short-channel effect, the double differential pairs with a source-degeneration structure are adopted, as shown in Fig. 2. In the proposed structure, two different values of re- sistors and are used for each differential pair, and the

         where , , , and . Thus, under ideal matching, the differential output current would be the function of the input signals

         (6)

         where is the th-order harmonic component provided by the th transistor of the proposed structure, , and . Although the resistors connected to the source of a single pseudodifferential pair degrade the lin- earity performance, the third-order harmonic component could be cancelled out by proper sizing of the double pseudodifferen- tial pairs through a Taylor series expansion of (6) to yield

         This expression can be obtained by giving

         (8)

         were , , and is the width, length, and transconduc- tance of the th transistor, respectively, and is the th short- channel equivalent resistance. Under the minimization of the third-order harmonic component, the transconductance of the proposed structure is given by

         (9)

         The transconductance decreases because of introducing the double differential pairs and the source-degeneration resistors. This implies higher linearity with the tradeoff of higher power consumption.

      3. Design Methodology

      In order to obtain high-linearity performance for the double differential pair structure under optimal transconductance effi- ciency, a simple approach is used by giving the ratio of param- eters to represent the circuit operation. Thus, by giving

      (10)

      we can find that the ratios of (10) would be used to define the transconductance efficiency compared with the single differen- tial-pair circuit and the third-order harmonic component of the proposed circuit. In addition, the ratio values should be designed within practical implementation boundary. Bandwidth, noise performance, and matching are also taken into consideration.

      The optimization procedure starts from the reduced transcon- ductance value. We define that less then 30% of the transconduc- tance should be reduced with respect to that of a single differen- tial-pair circuit with the same size and current consumption. From Fig. 3, we can find that, if the value of is set to 3 under large , we can obtain less than 30% reduction of the transconductance. Moreover, if the value of 4 for is used, less than 25% reduc- tion of the transconductance would be obtained. Fig. 4 shows the third-order distortion component of the proposed design. In order to obtain minimized distortion components, the ratio is chosen as 9 while is set to 3. If is set to 4 for less transconductance reduction, should be set to 16, but such a large ratio would de- grade the bandwidth performance owing to the large parasitic ca- pacitance of input transistors. After the optimization procedure, the optimal ratios of the proposed circuit would be given by

      (11)

      The optimization procedure concludes that the third-order dis- tortion component is ideally cancelled out with the expected

      Fig. 3. Optimal parameter evaluation for the reduced transconductance.

      Fig. 4. Optimal parameter evaluation for the third-order harmonic component.

      transconductance value, as shown in Fig. 5. The linearity per- formance is actually robust to process variation owing to the flat distribution in Fig. 4. Thus, the small reduction of the transcon- ductance value makes high linearity and high speed possible under about 30% of extra power consumption.

      Transconductance tuning would be another important issue in the OTA design. The main idea of the transconductance tuning is to compensate for the variation caused from fabricated process and temperature. Fig. 5 shows the contour plot of the third-order harmonic component under transconductance tuning, resulted from Fig. 4. We can find that, if is changed from 1 to 4 when is set to 9, it implies more than 300% of the transconductance tuning range, as shown in Fig. 3, and the third-order harmonic component value of less than 0.001 can be guaranteed, as illus-

      trated in Fig. 5.

   3. PROPOSED OTA CIRCUIT

      1. Implementation of the Linearization Technique

         Fig. 6 shows the proposed OTA design. Two differential pairs M1M2 and M3M4 are used in order to cancel the nonlinearity component, as described in the previous section. For continuous

         Fig. 5. Contour plot for the third-order harmonic component under transcon- ductance tuning.

         Fig. 6. Proposed OTA circuit.

         transconductance tuning strategy, transistors M5M8 operating in the linear region are used to replace the resistors. The equiv- alent resistance is given by

         (12)

         where is the gate voltage of the transistor. Therefore, we can obtain the required equivalent resistance by applying the voltage and to yield

         (13)

         (14)

         The linearity can be maintained by proper sizing of the de- generated transistors and the control voltage. In addition, the tuning ability of the proposed circuit can be achieved by ad- justing the control voltages and . Fig. 7 shows the simu- lated large-signal transconductance of the differential OTA op- erating in a 1.5-V supply voltage. The proposed circuit can be tuned from 360 to 470 S. It can be noticed that the transcon- ductance tuning range is limited by the linear-region operation of transistors M5M8. Besides, the speed of the proposed OTA is mainly limited by the parasitic capacitors caused by the cur- rent mirror circuits.

         Fig. 7. Simulated transconductance tuning range.

      2. Common-Mode Stability

      The OTA shown in Fig. 6 requires a proper common-mode control system due to the pseudodifferential structure [14], [15]. The common-mode control system includes the common-mode feedforward (CMFF) circuit and the common-mode feedback (CMFB) circuit. The CMFF circuit should be used with the CMFB circuit for output common-mode voltage stabiliza- tion. Fig. 8 shows the circuit of the common-mode control system. For the CMFB circuit, the input transistors MF1MF4 perform the tasks of the common-mode detection and refer- ence comparison. If the common-mode voltage of the OTA output signal equals the desired common-mode voltage , then the total current through MF7 will be constant and the common-mode bias voltage VCM is fixed. On the other hand, if the common-mode voltage of the OTA output signal is not the same as , a current will be mirrored by MF9 to change VCM adaptively. Thus, the feedback mechanism adjusts the output common-mode voltage to the desired value.

      Furthermore, the input common-mode control circuitry is formed by transistors MF14MF18 that constitute the CMFF circuit. The combination of transistors MF14 and MF15 gen- erates a scaled copy of input common-mode currents, which is subtracted at the OTA output stage through the use of current mirror MF17MF18. Thus, the input common-mode signal could be suppressed out and only the differential-mode signal appears at the output stage. As the mechanism shown above, it is demonstrated the common-mode control circuit can be implemented to achieve excellent stability over the tuning range. Moreover, linearity could be maintained by the robust and stable common-mode control system.

      The common-mode rejection (CMR) depends on matching. We can define a matching factor of ( ) between the

      CMFF path and the signal path, where is the mismatch

      ratio. We can emulate the CMFB circuit as a small resistor of value , and then the common-mode gain

      of at low frequency can be obtained, where is obtained from (9), is the transconductance of transistors M17 and M18, and is the output conductance of the OTA. This is the result of the combined CMFB and CMFF systems. Because is large and is much less than unity,

      even mis- match problems occur so that high CMR can be obtained.

      Fig. 8. Common-mode control system.

   4. NONIDEALITY ANALYSIS OF THE IMPLEMENTATION

      1. Mismatch

         Owing to the nonideal matching phenomena of MOS tran- sistors, the nonlinearity cancellation is not perfect and second- order harmonic distortion components would still appear at the differential output nodes. For the double differential-pair struc- ture, it is assumed that there are mismatches of

         for transistors M1 and M2 and for transistors M3 and M4. Repeating the analysis of (6), we can find that the second-order distortion component resulted from mismatch is given by

      2. Thermal Noise

      For the high-speed circuit, the most significant noise source of a single transistor is the thermal noise rather than the flicker noise. The channel noise can be modeled by a current source connected between the drain and source with a spectral density

      (16)

      where is the Boltzmann consant, is the absolute temper- ature, is the source conductance, and the device noise pa- rameter depends on the bias condition [16]. Using the thermal noise model, the total output-referred noise spectral density of the double differential pairs with degeneration structure is de- rived as

      (15)

      Therefore, the distortion components caused by transistor mis- match could be minimized by applying large degenerated re- sistors and gate overdrive voltage. Besides, the current mirrors M9M12 would also contribute second-order distortion compo- nents under the proposed degenerated structure, and thus large device sizes and small aspect ratios would be designed. From the simulation with 2% transistor mismatch, the highest even- order components remain lower than odd-order components by at least 5 dB. In addition, careful layout was taken while the de- vice match is required. The error output current contributed by transistor mismatch can be divided by the overall transconduc- tance to model an equivalent offset voltage, and it could be re- moved by applying an offset voltage of input differential signals.

      (17)

      where and would be the noise parameter at saturation and linear regions, respectively. The input-referred noise spectral density could be calculated by dividing the output- referred noise

      Fig. 9. Die microphotograph.

      spectral density by the overall OTA transconductance. From the noise analysis, large aspect ratios of input transistors and small aspect ratios of load transistors should be designed. The input-referred noise of the proposed circuit is higher than the single differential-pair circuit owing to the fact that the noise contribution is the combination of two input differential pairs. Moreover, the degenerated MOS resistors contribute additional noise sources to the proposed circuit.

   5. EXPERIMENTAL RESULTS

      The proposed OTA has been fabricated with TSMC 180-nm deep n-well CMOS process. It has been measured to verify its operation and to evaluate the linear characteristics. A mi- crophotograph of the linear OTA is depicted in Fig. 9, and the oc- cupied area is 15.1 mm . A supply voltage of 1.5 V was employed in the measurements, and the nominal static power consumption of the OTA is 9.5 mW. The required supply voltage for the circuit is (saturation region), and 1.5 V is suf- ficient for this circuit to operate under 180-nm CMOS process. For the measurement setup, the output signal of the signal generator was past through a low pass filter for the spectral purity of the input signal. The transformers were used before and after the input and output terminals for single-to-differ- ential and differential-to-single conversion for the differential circuit. The output signal was measured with a spectrum ana- lyzer. The third-order inter-modulation (IM3) distortion mea- sured with two sinusoidal tones of 0.9- amplitude is shown in Fig. 10. The IM3 is shown to be about 60 dB at a speed of 40 MHz. Fig. 11 shows the nonlinearity behavior with re- spect to the frequency under the same input swing range. At low frequencies, the IM3 of dB could be obtained. More- over IM3 less than ould be achieved for a frequency up to 60 MHz. The increment of the IM3 is due to the different high frequency behaviors of the two input differential pairs. The measured input referred noise spectral density at 40 MHz is

      Fig. 10. Measured two-tone inter-modulation distortion.

      Fig. 11. Measured two-tone inter-modulation distortion with respect to input signal frequency.

      nV Hz. Table I summarizes this work with recently re- ported works. In order to compare with different implementa-tions of OTAs, the defined figure of merit (FOM), which takes the transconductance value, linearity performance, speed of the implemented circuit, input swing range, and power consump- tion into account, is expressed as follows:

      (18)

      Therefore, our high-speed linear OTA compares favorably with the literature.

   6. CONCLUSION

      An approach to enhance the OTA linearity under nano-scale technology has been proposed, and the experimental result proves the same linear characteristic by the fabricated

      chip. By taking the short-channel effect into consideration under small feature sizes, this approach is based on the nonlinearity cancellation scheme with two pseudodifferential pairs of the source-degeneration structure, and the circuit performs well at high frequencies. The MOS transistors working in the linear region were used to replace the poly resistors. It not only saves the chip area but also adds the tuning ability. A common-mode control circuitry, including the CMFF and CMFB circuits, is used for the input and output common- mode stability. The measurement results show about 60-dB IM3 with 40-MHz

      0.9- input signals under a 1.5-V supply voltage.

      ACKNOWLEDGMENT

      The authors would like to thank the National Chip Implemen- tation Center of Taiwan for supporting the chip fabrication.

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