,
2 2 2 2 2 2
R 2 3 3 2 5 5 R
eq f mR MR MR mR eq
v = g v + v g (3.89)
( )
R ,
2
3 5
4 2
eq th c mR mR d mRS
I = kT γ g +g +γ g (3.90)
Thus, the optimized values versus the noise and linearity performance would be chosen and adopted carefully from their performance tradeoff.
3.3.4 Filter architecture
To demonstrate the basic building block in a system level, a fifth-order Elliptic Figure 3.18. Fifth-order elliptic RLC ladder network prototype.
Figure 3.19. Fifth-order Elliptic low-pass Gm-C filter.
low-pass filter is implemented [42]. The fifth-order Elliptic low-pass filter design starts from a standard fifth-order Elliptic low-pass LC-ladder prototype, as shown in Fig. 3.18. A -6dB DC gain can be easily obtained under very low frequency when resistor RS equals to resistor RL. From the RLC-ladder prototype, through the use of the signal-flow graph method [43], the fifth-order Elliptic low-pass Gm-C filter, which consists of seven identical OTAs and seven capacitors, including two floating capacitors, is obtained. The transconductance, which equals to the value of 1/RS and 1/RL, is used for all OTAs. Q tuning circuits are not considered here with the intrinsic quality of the low Q structure. The final Gm-C filter implementation is shown in Fig.
3.19. The OTA introduced in the previous section is used here in the design of the fifth-order Elliptic low-pass Gm-C filter.
In low-pass filter design, the cutoff frequency of the filter is proportional to gm/C, where gm is the transconductance of the OTA and C is the capacitance. Low cutoff frequency filters are very important in the speech signal processing and medical hearing application. However, there are some problems encountered in these low frequency filter design. The main issues are the large time constant involved and the values of the resistors and capacitance limited by the silicon area. In our circuit, when the transconductor works in the weak inversion region, a small value of capacitance will be enough to achieve the low cutoff frequency owing to the small transconductance in the nS order. On the other hand, the larger transconductance can also be obtained in the same filter architecture for higher cutoff frequency when the OTA works in the saturation region.
The cutoff frequency of the Gm-C filter is tuned by changing the DC bias current of the OTA. Because the transconductance range of the OTA is quite wide, the resultant filter also has a wide cutoff frequency range under suitable working mode selection.
Tuning circuitry can be developed with digitally controlled circuits in a system-on-a-chip solution by choosing a number of current sources for Gm tuning.
The maximum capacitance shown in Fig. 3.19 is only 3.6 pF, so it is easy to integrate with the other circuits.
(a) OTA in the weak inversion region.
(b) OTA in the multi-inversion regions: the input stage stays in the weak inversion region while the output stage operates from the weak inversion region to the strong
inversion region.
(c) OTA in the strong inversion region.
(d) OTA in the multi-inversion regions: the input stage stays in the strong inversion region while the output stage operates from the strong inversion region to the weak
inversion region.
Figure 3.20. The measurement results of the proposed transconductor circuit.
3.3.5 Experimental results
The OTA and the filter were fabricated in the TSMC 0.18-µm Deep N-WELL CMOS process. Body effects can be simply eliminated by connecting the source and the bulk terminals together in the process. The aspect ratio of 11.5 µm/2 µm is used for transistors M1, M2, M3, M4, M5, and M6, and 11.5 µm/0.2 µm is used for transistors M7, M8, and M9. The value of 8 µm/4 µm is used for MR5 and MR6, and Iref is equal to 20 µA in the equivalent resistor circuit. 1 µm/1 µm is used for linear region MOS resistor MRS. Since the mismatches in transconductors and capacitors directly translate to the degradation of overall performance, such as nonlinear effects and errors of transformation, the filter has been laid out very carefully.
Metal-insulator-Metal capacitors were used in the circuit and the unit of the capacitor array is 0.1 pF. In this section, the experimental results are presented. All of the results were obtained with a single power supply of 1.8 V.
The measurement results of the OTA’s transfer curves are shown in Fig. 3.20(a), 3.20(b), 3.20(c) and 3.20(d). In Fig. 3.20(a), the measurements of voltage to current transfer curves are obtained when both the input and output stages of the OTA operate in the weak inversion region as IC1 equals to 10 nA and IC2 changes from 10 nA to 80 nA. The saturated resistor circuit is selected here by setting Vmode to GND. The transfer curves in the weak inversion region follow the expected formula described previously. Also, the transconductance is changed from 2.5 nS to 16 nS, as shown in the figure. In Fig. 3.20(b), owing to the increment of IC2, the output stage of the OTA extends the operation from the weak inversion region to the strong inversion region while the input stage and the equivalent resistor remain in the same previous condition, and thus achieves to a much larger transconductance. The measured transconductance could be tuned from 3 nS to 610 nS by increasing IC2 to the value of 10 µA.
In Fig. 3.20(c), the input and output stages of the OTA both operate in the strong inversion region to achieve a large transconductance, as compared with the weak inversion region operation. The linear region MOS resistor circuit is selected here by setting Vmode to VDD. The transconductance from 11 µS to 18 µS is obtained while the current IC1 equals to 1 µA and IC2 changes from 10 µA to 40 µA. We can find that the transconductance would be tuned proportional to the square root of IC2 as described in the formula above. In Fig. 3.20(d), the decreased IC2 results that the output stage of the OTA extends the operation from the strong inversion region to the weak inversion region while the input stage and the equivalent resistor remain in the same condition, and thus achieves to a much smaller transconductance. As shown in
the figure, the transconductance could be tuned from 20.2 µS to 0.19 µS by decreasing IC2 to the value of 0.5 µA.
From the measurement results of Fig. 3.20(b) and 3.20(d), continuous tuning from weak inversion operation to strong inversion operation can be guaranteed and the OTA can be tuned for a very wide range. However, the linearity of the OTA should be maintained over the range because it will directly affect the linearity of the proposed Gm-C filter. For the linearity of this OTA, when both the input and output stages of the OTA operate in the weak inversion region, THD is about -56 dB with IC1 = 10 nA IC2 = 10 nA at 100 Hz 300 mVpp input signal. As IC2 increases to 10 µA, the output stage will operate in the strong inversion region while the input stage stays in the weak inversion region, and THD is measured to be -44 dB. On the other hand, when the input and output stages of the OTA operate in the strong inversion region, THD of -43 dB is measured by giving IC1 = 1 µA and IC2 = 40 µA with 10 KHz 300 mVpp
input signal. Input signals with higher frequency are applied here owing to the fact that the large transconductance would be used for the filter with higher cutoff frequency. As IC2 decreases to 0.5 µA, the output stage of the OTA operates in the weak inversion region while the input stage stays in the same region, and THD of -42 dB is measured.
Figure 3.21. Measured frequency responses over the tuning range.
Figure 3.22. Measured IM3 values at cutoff frequency.
Fig. 3.21 illustrates the filter measurement results over the tuning range for different bias currents IC1 and IC2. The cutoff frequency can be tuned from 250 Hz to 1 MHz, a tuning ratio of 4000. The third-order inter-modulation distortion, which implies the linearity performance of the proposed filter, is measured at cutoff frequency. By using two sinusoidal tones with the amplitude of 300 mVpp, -53 dB is measured when the filter operates at low cutoff frequency of 250 Hz. On the other hand, when the cutoff frequency of the filter is tuned to 1 MHz, the IM3 is measured -41 dB. Fig. 3.22 shows the relationship of measured IM3 versus cutoff frequency for the proposed wide tuning range filter. The worst case which happens in the middle band of the wide tunable filter is due to the multi-inversion operation.
When the cutoff frequency of the filter is 250 Hz, a dynamic range of 52 dB is measured with the 300 mVpp input signal as Vmode is set to ground voltage. On the other hand, at the cutoff frequency of 1 MHz, a 48 dB dynamic range is measured as Vmode is set to VDD voltage. The measured PSRR at 100Hz is 36 dB. The filter dissipates 0.2 mW and 0.8 mW for lowest and highest cutoff frequency setting, respectively, at 1.8 V supply voltage.
A die photo is shown in Fig. 3.23. The total active area is less than 0.3 mm2. In order to compare with different implementations of Gm-C low-pass filters, the figure of merit defined in [44], which takes the inter-modulation free dynamic range, speed
of the implemented filter, tuning ratio, and normalized power consumption into account, is expressed as follows:
linear N
10 log(IMFDR fo tuning)
FoM power
× ×
= (3.91)
where IMFDR is defined as the signal to noise ratio when the power of the third-order inter-modulation distortion term equals to the noise power, fo is the geometrical mean
TABLEI
PERFORMANCE SUMMARY OF THE FABRICATED PROTOTYPE
Technology TSMC 0.18-µm CMOS
Supply Voltage 1.8V
Filter type Fifth-order Elliptic low-pass
Tuning range 250Hz-1MHz
IM3 for 300mVpp
input signals over the tuning range
-40dB
Dynamic range 48 dB
Power consumption 0.8mW
Active area 0.3mm2
Figure 3.23. Die microphotograph.
Figure 3.24. FOM comparison with previously published filters.
of the cutoff frequency in the unit of Hz, tuning is the tuning ratio of the low-pass filter, and powerN is the geometrical mean of power per pole quantity in the unit of Watt. The FOM of the filter is plotted versus power supply voltage and compared with the other previously published works. As shown in Fig. 3.24, our wide tuning range low-pass filter compares favorably with the literature. Table 3.1 summarizes the experimental results of the proposed filter. could be set and the transconductance could be continuously tuned by setting IC1 and IC2. With the use of the OTA as a building block in the filter architecture, the cutoff frequency of the low-pass filter is changed from 250 Hz to 1 MHz, which covers the range of some audio, speech, bio-medical, and wireless application, so it could be used in multi-mode applications of signal processing. Moreover, the silicon area is saved with less power consumption in the entire filter design. The minimum power supply needed is in the range of 2VGS +VDSsat which can be around 1.2 V or less depending on bias current levels. Measurement results demonstrate the potential of the technique to provide a system-on-a-chip design solution for low power dissipation
Table 3.1. Performance summary of the fabricated prototype.
Technology TSMC 0.18-µm CMOS
and very wide tuning range applications.
Figure 4.1. The Basic diagram of the direct-conversion receiver.