High-Frequency Low-Current Second-Order Bandpass Active Filter Topology and Its Design in 28-nm FD-SOI CMOS

Abstract

Fully Depleted Silicon on Insulator (FD-SOI) CMOS technology offers the possibility of circuit performance optimization with reduction of both topology complexity and power consumption. These advantages are fully exploited in this paper in order to develop a new topology of active continuous-time second-order bandpass filter with maximum resonant frequency in the range of 1 GHz and wide electrically tunable quality factor requiring a very limited quiescent current consumption below 10 μA. Preliminary simulations that were carried out using the 28-nm FD-SOI technology from STMicroelectronics show that the designed example can operate up to 1.3 GHz of resonant frequency with tunable Q ranging from 90 to 370, while only requiring 6 μA standby current under 1-V supply.

1. Introduction

Fully Depleted Silicon on Insulator (FD-SOI) CMOS technologies provide several advantages in comparison to bulk CMOS, namely: (1) unparallel threshold voltage tuning range from the back gate, which allows effective trimming strategies for process and temperature compensation, (2) better threshold voltage matching, (3) low parasitic capacitances, (4) high transition frequency, f_T, of hundreds of gigahertz, and (5) improved intrinsic dc gain [1]. These behaviors, together with the increased flexibility offered by the MOS “fourth terminal”, have enabled many ingenious and innovative integrated-circuit (IC) solutions in analog, radio frequency (RF), millimeter wave (mW), and mixed-signal systems also for automotive, IoT, 5G, and emerging applications [2,3,4,5].

Ubiquitous RF portable communications need ultra-low-power IC solutions that are able to prolong battery life and recharging cycles in energy harvested devices [6,7,8]. In these applications fundamental building blocks are continuous-time filters with tunable cutoff frequency and small fractional bandwidth. At this purpose, several IC implementations have been developed that exploit inductors, transformers, resonators, transmission lines, etc. [9,10,11,12,13,14,15,16]. These solutions usually require current consumptions in the order of several milliamperes in order to provide the required high frequency performance and frequently exploit nonstandard approaches for the CMOS technology.

This paper addresses the problem of designing a monolithic inductorless second-order band-pass active filter that is suitable for RF portable applications providing electrical tunability of both the resonant frequency and quality factor, under a very limited quiescent current budget constraint of a few microamperes. This result is achieved thanks to the low parasitic capacitances and high f_T offered by the FD-SOI CMOS technology and through the extensive use, as a design option, of the body terminals of transistor devices [17,18,19]. No particular application has been targeted, as the purpose of this document is simply to introduce a new topology and show its potential. To this end, a preliminary design example was developed and simulated while using STMicroelectronics 28-nm process. The filter consumes 6 μA of dc current from a single 1-V power supply while providing a resonant frequency of 1.3 GHz and tunable quality factor ranging from 90 to 370. Simulated 1-dB compression point, P_1dB, and input referred third-order intercept point, IIP3, were −20.5 dBm and −9.23 dBm, respectively. The noise Figure was found to be 31 dB.

2. The Proposed Solution

2.1. Circuit Description

Figure 1 shows the circuit schematic of the proposed band-pass filter. It is made up of common source transistor M1 implementing a first (inverting) gain stage biased by current generator M5. The input signal is AC coupled to the gate of M1 through capacitor C_IN and the output of the filter is taken at the drain of M1 which drives also the second (noninverting) gain stage made up of common source transistor M2 and unitary current mirror M3–M4 biased by current generator M6. Transistors M7–M11 are used for biasing purposes. Negative feedback is accomplished by connecting the second stage output (drains of M4 and M6) to the bulk of M1. This loop also provides DC stabilization by setting the second stage output voltage to around V_G11 thanks to the gate-bulk connection of M11 and circuit symmetry. The bulk of M2 is used for tuning the filter quality factor, Q, through voltage V_B, as we will show in the followings.

2.2. Circuit Analysis

Figure 2 illustrates the simplified small-signal equivalent circuit of the proposed solution, where g_mi and g_mbi are the gate-source and source-bulk transconductances of the i-th transistor. C_db1 is the drain-bulk capacitance of M1 and r_o1, r_o2 and C_o1, C_o2 are, respectively, the equivalent resistances and capacitances at the nodes o1 and o2 (being o1 the filter output terminal. The expressions of these small signal parameters are given below

$$r_{o1}=r_{d1}\Vert r_{d5}$$

(1a)

$$r_{o2}=r_{d4}\Vert r_{d6}$$

(1b)

$$C_{o1}=C_{gs2}+\left(1+g_m{}_2/g_m{}_3\right)C_{gd2}+C_{db5}+C_{gd5}+C_{gd1}$$

(1c)

$$C_{o2}=C_{db4}+C_{db6}+C_{bs1}+C_{gd4}+C_{gd6}$$

(1d)

We will show that C_o1 and C_o2 play an important role in setting the filter resonant frequency while C_db1 is fundamental in the selection of Q. Observe that AC coupling capacitance C_IN is neglected here, as its effect is well known; indeed, it introduces a zero at ω = 0 and a low-frequency pole $p_{IN}=-g_{m11}/C_{IN}$ in the input-output transfer function.

After standard calculation and neglecting higher-order terms, the resulting transfer function V_o1/V_i is given by

$$H\left(s\right)=\frac{V_{o1}}{V_i}\approx -\frac{g_{m1}{r}_{o1}}{1+g_{mb1}{g}_{m2}{r}_{o1}{r}_{o2}}\frac{1+s{r}_{o2}\left(C_{o2}+C_{db1}\right)}{1+a_{1}s+a_2{s}^2}$$

(2)

where

$$a_1=\frac{C_{db1}\left[r_{o1}+r_{o2}+\left(g_{mb1}-g_{m2}\right)r_{o1}{r}_{o2}\right]+r_{o1}{C}_{o1}+r_{o2}{C}_{o2}}{1+g_{mb1}{g}_{m2}{r}_{o1}{r}_{o2}}$$

(3a)

and

$$a_2=\frac{r_{o1}{r}_{o2}\left[C_{db1}\left(C_{o1}+C_{o2}\right)+C_{o1}{C}_{o2}\right]}{1+g_{mb1}{g}_{m2}{r}_{o1}{r}_{o2}}$$

(3b)

Assuming g_mb1g_m2r_o1r_o2 >> 1, the outband filter gain, H_ob, is from (2)

$$H_{\mathrm{ob}}=\frac{g_{m1}{r}_{o1}}{1+g_{mb1}{g}_{m2}{r}_{o1}{r}_{o2}}\approx \frac{g_{m1}}{g_{mb1}{g}_{m2}{r}_{o2}}$$

(4)

which becomes conveniently less than 1, provided that g_mb1r_o2 > g_m1/g_m2, a condition that is usually met.

Under the same assumption, g_mb1g_m2r_o1r_o2 >> 1, the resonant angular frequency, ω_o, and quality factor are respectively given by

$${\omega }_o=\frac{1}{\sqrt{a_2}}\approx \sqrt{\frac{g_{mb1}{g}_{m2}}{C_{db1}\left(C_{o1}+C_{o2}\right)+C_{o1}{C}_{o2}}}$$

(5a)

$$Q=\frac{\sqrt{a_2}}{a_1}\approx \frac{\sqrt{g_{mb1}{g}_{m2}\left[C_{o1}{C}_{o2}+C_{db1}\left(C_{o1}+C_{o2}\right)\right]}}{\left[r_{o1}+r_{o2}+\left(g_{mb1}-g_{m2}\right)r_{o1}{r}_{o2}\right]C_{db1}+r_{o1}{C}_{o1}+r_{o2}{C}_{o2}}{r}_{o1}{r}_{o2}$$

(5b)

The above expressions can be further simplified as a result of the straightforward design strategy that takes advantage of similar transistor dimensions and bias currents for the two common-source stages in order to gain further insight into the above equations useful during the design phase. In this case, we can set r_o1 = r_o2 = r_o1,2 and, somehow, oversimplifying, C_o1 $\approx$ C_o2 = C_o1,2, yielding

$${\omega }_o\approx \frac{\sqrt{g_{mb1}{g}_{m2}}}{C_{o1,2}}\frac{1}{\sqrt{1+2C_{db1}/C_{o1,2}}}\approx \frac{\sqrt{g_{mb1}{g}_{m2}}}{C_{o1,2}}$$

(6a)

$$Q\approx \frac{\sqrt{g_{mb1}{g}_{m2}}}{2}{r}_{o1,2}\frac{\sqrt{1+2C_{db1}/C_{o1,2}}}{1+\left[1+\left(g_{mb1}-g_{m2}\right)r_{o1,2}/2\right]C_{db1}/C_{o1,2}}\approx \frac{1}{2}\frac{\sqrt{g_{mb1}{g}_{m2}}{r}_{o1,2}}{1+\left[1+\left(g_{mb1}-g_{m2}\right)r_{o1,2}/2\right]C_{db1}/C_{o1,2}}$$

(6b)

The approximated expression in (6a) shows that ω_o is determined by the ratio of the square root of g_mb1g_m2 to C_o1,2, as C_db1 is intrinsically lower than C_o1,2 and, consequently, 2C_db1/C_o1,2 can be neglected with respect to the unity. This condition can be also ensured by adding parallel capacitances to C_o1 and C_o2 at the expense of a proportional reduction of ω_o that, in this way, can be decreased by several decades, offering wide range of frequency application. Of course, C_IN must be increased accordingly to set the input pole well below the resonant angular frequency. However, (6a) indicates that, to maximize ω_o for a given transconductance level of g_m2 and g_mb1 (observe that g_mb1 is a known fraction of g_m1), the design effort should be aimed at minimizing C_o1,2.

It is also to be noted that ω_o can be finely and continuously tuned by varying the transconductances in (6a) by varying, in turn, the DC current I_B in Figure 1. Once ω_o is set, (6b) shows that also Q is set because both ω_o and Q depend on the same parameters. It is seen that, due to the minus sign in the denominator of (6b), very high Q values can be achieved. Indeed, the term proportional to g_mb1 − g_m2 is negative and tends to reduce the denominator. However, because Q must be positive to preserve stability, the following condition (7) must be ensured. In other words, Q tends to be infinitely large and then becomes negative if the first member of (7) approaches the second member and overtakes it. Additionally, in this case, if it is required to fulfil (7), additional capacitances in parallel to C_o1,2 may be added.

$$g_{m2}-g_{mb1}<2\frac{1+C_{o1,2}/C_{db1}}{r_{o1,2}}$$

(7)

Some of the above considerations can be gained with the aid of Figure 3a,b, which, respectively, depict the normalized resonant frequency, ω_on, and normalized quality factor, Q_n, defined in (8a) and (8b) versus C_db1/C_o1,2, and where g_mb1, g_m2, and r_o1 were set to 1.4 μA/V, 19 μA/V, and 2 MΩ, respectively.

$${\omega }_{on}={\omega }_o/\left(\sqrt{g_{mb}{}_1{g}_{m_{2,4}}}/C_{o1,2}\right)=1/\sqrt{1+2C_{db1}/C_{o1,2}}$$

(8a)

$$Q_n=Q/\frac{\sqrt{g_{mb1}{g}_{m2}}}{2}{r}_{o1,2}\approx \frac{\sqrt{1+2C_{db1}/C_{o1,2}}}{1+\left[1+\left(g_{mb1}-g_{m2}\right)r_{o1,2}/2\right]C_{db1}/C_{o1,2}}$$

(8b)

The light dependence of ω_on on C_db1/C_o1,2 can be appreciated from Figure 3a, which shows a 5% decrease as a result of a change in C_db1/C_o1,2 from 0 to 0.06. In contrast, the strong dependence of Q_n on C_db1/C_o1,2 is apparent from Figure 3b, which shows the expected asymptote given by (7) when its first member equals the second member.

Because the high Q values achievable lead to a high circuit sensitivity to process tolerances and temperature variations, additional circuitry must be added to control this parameter, the development of which is beyond the scopes of this paper. From (6b) or (8b), it is seen that a possible way to provide continuous Q tunability is via g_m2, which, in turn, can be electrically varied through V_B in Figure 1. Observe that changing g_m2 has a limited impact onto ω_o because g_m2 >> g_mb1, as will be shown in the next simulations section.

3. Validation Results

The proposed solution was designed in the 28-nm FDSOI technology provided by STMicroelectronics. Power supply was set to 1 V and transistor dimensions were set in order to achieve a resonant frequency of around 1 GHz with Q > 100, under a very limited current consumption of 6 μA (1 μA for each branch, including the reference one). The chosen design values and main small signal parameters are summarized in

Table 1. Design parameters used in simulations.

Parameter	Value [nm/nm]	Parameter	Value [nm/nm]
(W/L)1	180/90	(W/L)9	360/90
(W/L)2	315/90	(W/L)10	360/90
(W/L)3	360/90	(W/L)11	180/90
(W/L)4	360/90	CIN	200 fF
(W/L)5	360/90	VDD	1 V
(W/L)6	360/90	IB	1 μA
(W/L)7	360/90	VB	0.5 V
(W/L)8	360/90

and

Table 2. Small signal parameters.

Parameter	Value
gm1 = gm11	18.1 μA/V
gmb1	1.4 μA/V
gm2	18.9 μA/V
ro1	2.03 MΩ
ro2	2.01 MΩ
Co1	640 aF
Co2	450 aF
Cdb1	30 aF
CIN	200 fF

, respectively.

Using the values in Table 2 and the expressions that are found in Section 2.2, the low-frequency pole due to C_IN results at around 14.4 MHz. The outband gain from (4) results to be 0.33 (−9.6 dB). The expected resonant frequency from (5a) is 1.46 GHz with expected quality factor from (5b) of 180. Note that the inaccurate estimation of C_o1,2 may lead to strong errors, given the extreme sensitivity of this parameter. Figure 4 depicts the Bode plots (magnitude and phase) of the simulated circuit transfer function, which shows 2πω_o = 1.33 GHz and Q = 164. The peak gain is 54.5 dB and the outband gain is −13 dB.

Figure 5a shows Bode plot magnitude for three different bias currents I_B, namely 0.9 μA, 1 μA, and 1.1 μA. It is seen that the resonant frequency is shifted, respectively, from 1.24 GHz to 1.33 GHz and to 1.42 GHz. As an expected but unwanted effect of frequency tuning, the quality factor also changes from 312 to 164 and to 112. Equalization of the quality factors is possible through voltage V_B, as explained in the previous section and illustrated in Figure 5b, where V_B equal to 173 mV, 500 mV, and 904 mV is used to tune g_m2 and achieve the same Q value of 164 in the three cases.

Figure 6 shows the plot of achieved resonant frequency and quality factor as a function of voltage V_B in the nominal condition I_B = 1 μA in order to better appreciate the Q tuning interval offered by the proposed design. It is seen that Q can be varied from around 90 to 370, while no appreciable change in the resonant frequency is produced.

The effect of temperature was simulated under three different conditions, namely −10 °C, 27 °C, and 85 °C. The obtained magnitude Bode plots are shown in Figure 7a. ω_o/2π and Q are respectively 1.43 GHz and 353@−10 °C, 1.33 GHz and 164@27 °C, and 1.20 GHz and 95@85 °C. These limited variations are within the tuning range seen before and they can be counteracted by the use of concurrent I_B and V_B tuning. Figure 7b shows the result after Q tuning to the value of 164 by setting V_B equal to 17 mV@−10 °C, 500 mV@27 °C, and 963 mV@85 °C.

Figure 8a,b show, respectively, the filter 1-dB compression point, P_1dB, and third-order intercept point, IP3. The value of P_1dB is −20.5 dBm and input-referred IP3 is −9.23 dBm. Noise Figure was 31 dB and spurious free dynamic range, SFDR, was 71.6 dBm.

Linearity was evaluated under −50 dB input power. The third-order intermodulation distortion, IMD3, was found to be −79 dBm and it was simulated by a two-tone test with 11 MHz spacing at 1.33 GHz, within the band of interest.

Table 3. Comparison with the state of the art.

	This Work a	[22]	[23]	[24]	[20]	[21] a
Technology	28 nm FDSOI	0.35 μm	0.5 μm	0.5 μm SOI	0.18 μm	45 nm
Filter order	2	2	2	2	2	2
Resonant freq. (GHz)	1.33	2.19	0.9	2.5	2.44	2.511
Quality factor	164	43	45	36	60	69
Supply voltage (V)	1	1.2	3	3	1.8	±1
Power (mW)	0.006	5.2	39	15	10.8	0.168
Noise figure (dB)	31	26.8	21	6	18	29.62
P1dB (dBm)	−20.5	−30	−5.5	−15	−15	−1.5
FOM (dB)	87	49	67	80	71	92

^a Simulation results.

shows the summary and comparison of this work with other second-order band pass filters in the literature. A figure-of-merit, FOM, is also used for overall performance comparison [20,21]

$$FOM=\frac{N\cdot P_{1dB,W}\cdot f_o\cdot Q}{P_{dc}\cdot NF}$$

(9)

where N is number of poles (filter order), P_1dB,W is the in-band 1-dB compression point in watts, f_o is the resonant frequency, Q is the quality factor, P_dc is dc power consumption in watts, and NF is the noise figure (not in decibels). Higher FOM mean better performance. The proposed solution exhibits the lowest power consumption and lowest supply voltage, with FOM being one of the highest.

4. Conclusions

Although the “fourth” MOS terminal has been used for decades in the digital domain and even in the analog one [17,18], the body-source biasing was limited to only around 300 mV in order to avoid junction turn on and, hence, restricting the designer options and/or compatible supply voltage. The advent of FD-SOI technologies has made possible the full exploitation of the body as an independent terminal available to the designer, so that new circuits schemes that use the bulk with much more flexibility and efficiency can be developed. In this paper, a new micropower bandpass filter topology that exploits the MOS bulk terminal in the dc stabilization loop and also as a means of quality factor tuning is proposed and preliminary simulations are presented to show its potential in terms of achievable operating frequencies and quality factors. No particular application or standard has been targeted. Lower filter resonant frequency can be achieved by adding two capacitors at nodes o1 and o2 in Figure 2, whereas higher resonant frequency can be achieved by increasing the standby current. The main advantage of the solution is its high frequency capability requiring only a few microamperes of current consumption. The main drawback is related to the dependence of ω_o to the bulk transconductance, that is a fraction of the gate transconductance, thus limiting the maximum achievable ω_o. Further investigation is currently carried out to avoid this drawback as well realize a higher-order filter function with automatic tuning control for specific applications.