tors function as a high-pass filter, a low-pass filter, and a functions of the three filters for very long channel MOSFET feedback network, respectively. The authors ...
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Distributed MOSFET High-Pass Filters Wei Li,Student Member, IEEE, and Ezz I. El-Masry, Senior Member, IEEE Abstract-A new method for the analysis of distributed MOSFET filters is presented. The effects of parasitic capacitances on distributed high-pass MOSFET filters are investigated. Three schemes of MOSFET configurations functioning as distributed high-pass filters are presented and analyzed to demonstrate the new method and to illustrate the parasitic effects. The analyses are verified by the SPICE simulation and the very high frequency numerical model of a MOSFET given in [lo].
in reduced chip area and does not require separate capacitor structures [4]. It can be made by a widely used digital VLSI fabrication process, whereas conventional continuoustime or switched-capacitor techniques cannot. The operating frequency of a distributed MOSFET filter can be very high since the filter relies on internal transistor capacitances. Those capacitances are usually small compared to the separate capacitors used in other techniques, e.g., switchedcapacitor filters. However, there are some drawbacks in I. INTRODUCTION distributed MOSFET filters. An automatic tuning circuit MOS transistor, as a lumped element, has been mostly becomes necessary since the filters rely on internal transistor operated at below the intrinsic cutoff frequency. The capacitances. As the operating frequency approaches the distributed effect of a transistor at higher frequency is often intrinsic device cutoff frequency, the common CAD models considered as undesired. Actually, a MOS transistor is an for MOS transistors fail [4]. The method so far used to inherently distributed element. If the lumped element behav- analyze distributed MOSFET filter is the RC transmission ior is considered as characteristic of a MOS transistor at low line model. This is not convenient for filter designers. The frequencies, the distributed effect is just another nature of a obtained transfer functions of the filters are often very comMOS transistor at high frequencies. A circuit could be plicated [ 8 ] . To further explore the application of distributed designed so that some transistors work as lumped elements characteristics of a MOS transistor, we need a new method and some as distributed elements [3], [4]. Hence, it is that is simpler and also accurate enough to analyze the filter important not only to study how to avoid distributed effects characteristics. but also to explore how to make use of them. Some encouragThe small-signal high-frequency model for a four-terminal ing experimental results along this direction have been MOS transistor presented in [7] and [9] provides an effective reported [2]- [6]. tool to model the behavior of a MOS transistor at high A MOS transistor was first used by Khoury, Tsividis, and frequencies. A new method for analysis of high-pass disBanu [2] as a tunable distributed RC transmission line to tributed MOSFET filters, based on the four-terminal highrealize a low-pass function. A low-pass filter with an active frequency model of a MOS transistor in [7] and [9] is area of 0.006 m2 was demonstrated in [3]. The filter introduced in this paper. One can easily derive the transfer contains only four transistors as the circuit elements and function for a distributed MOSFET filter using this method operates at 40 MHz with very low power dissipation. Use of without any knowledge of the distributed RC filter theory. this kind of the filters can become a significant advantage in The involved parameters are all standard electrical, geometricases where a large number of filters must be implemented cal, and process parameters of a MOS transistor. Without on a chip. Also, a distributed MOSFET low-pass filter loss of accuracy, the obtained transfer function facilitates the has been successfully used in high-gain gigahertz band ampli- design of high-pass filters. In this paper, three schemes of fiers [ 6 ] . The filter provides a signal attenuation of greater MOSFET configurations functioning as high-pass filters are than 60 dB with near-zero phase shift at high frequencies. analyzed to demonstrate the proposed method and to illustrate Recently, a 100-MHz transistor-only low-pass filter and a the effects of parasitic capacitances. They will be referred to band-pass filter were presented [4]. The band-pass filter was as high-pass 1, high-pass 2 , and high-pass 3 hereafter. realized by three transistors and an amplifier. Three transis- (High-pass 2 was proposed in [4]). The biquadratic transfer tors function as a high-pass filter, a low-pass filter, and a functions of the three filters for very long channel MOSFET feedback network, respectively. The authors of [4] also of- are obtained using the new method. The characteristic frefered a generalization, which allows one to derive transistor- quency, the Q factor, and the high-frequency gain of only filters from a variety of known uniform RC structures, the filter are directly related to the standard MOSFET parausing a systematic procedure. A transistor-only filter results meters. It is found that the characteristic frequency of the filter is around three times the intrinsic cutoff frequency of a Manuscript received August 28, 1990; revised December 10, 1991. This work was supported by the National Science and Engineering Council of MOS transistor. To further increase the operating frequency Canada and the Canadian Network of Centres of Excellence in Microelec- of a distributed MOSFET filter, shorter channel length devitronics. This paper was recommended by Associate Editor M. Ismail. ces should be used. However, the parasitic capacitances can The authors are with the Department of Electrical Engineering, Technical then no longer be ignored. It is necessary to analyze how University of Nova Scotia, Halifax, NS, Canada B3J 2x4. the parasitic capacitances affects the behavior of the distriIEEE Log Number 9106627.
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buted high-pass filters for very-high frequency applications. It will be shown that when the junction capacitance of a MOSFET becomes large, high-pass 2 and high-pass 3 will not exhibit high-pass characteristics and only highpass 1 maintains its high-pass characteristics, regardless of effects of parasitic capacitances. To clearly demonstrate the proposed method and the effects of parasitic capacitances, we first concentrate on the analysis of the frequency characteristics of high-pass 1 in Section 11. The frequency responses of high-pass 2 and high-pass 3, as well as the comparison of the three filter configurations, are given in Section 111.
-b
- = F
vout
ground
(a)
T
11. MOSFET HIGH-PASS FILTER1
We propose a four-terminal network, with the gate and substrate of a MOSFET as the input terminal, the drain as the output terminal, and the source as an ac ground, as shown in Fig. l(a). It will be shown below that a distributed MOSFET connected this way realizes a high-pass function. A direct implementation of this structure would require floating bias voltage sources. A source-follower is used to overcome this difficulty. The chip implementation of the structure in Fig. l(a), including a source-follower, is given by Fig. l e ) . The P-channel source-follower provides both the dc bias and a buffered signal input to the gate, and is assumed to have very low output impedance [3]. The gate bias voltage is tuned by the control voltage V . The floating-substrate implementation in Fig. l requires the use of a P-well CMOS process. On an N-well process, the complementary of the circuit shown can be made. Notice that at very high frequencies the source'out follower in Fig. l(b) is bypassed due to direct feedthrough Vi, 'OV +'bde from the substrate to the gate of the distributed MOSFET. Hence the high-pass characteristics of the three-transistor circuit shown in Fig. l(b) will not deteriorate even at frequencies beyond the 3-dB cutoff frequency of the source(C) follower. The details of the SPICE simulation results are Fig. 1. (a) Schematics for single MOSFET high-pass filter 1. (b) A given in Section 2.3. MOSFET shown in (a) with the gate biased by a follower. (c) The The y-parameter equivalent circuit for high-pass filter 1 is y-parameter small-signal equivalent circuit of (a). shown in Fig. l(c). Capacitances C,,, Cb,, C,,,, and Cbse are not included since they are in parallel with the input voltage source. d The small-signal high-frequency model proposed by ? Bagheri and Tsividis [7] is shown in Fig. 2. The y-parameters of Fig. 2 were given in the form of a power series numerator over a common denominator series [7]. A single continuous expression was used for each model parameter. The various models with different upper frequency limits of validity can also be found in [7]. The model includes the transmission line effect of a MOS transistor at high frequencies and is valid in all range of operation (weak inversion, moderate inversion, strong inversion, nonsaturation, and saturation). The second-order model in [7] will be used in deriving the transfer functions in this paper.
Pin
A
--
2. I. Neglecting Parasitic Eflects In this section, the channel length of the transistor is assumed to be long enough so that the overlap and junction capacitances can be ignored. The remaining capacitance,
6 S
Fig. 2.
y-parameter small-signal model for an intrinsic four-terminal MOS transistor.
LI AND EL-MASRY: DISTRIBUTED MOSFET
between channel and gate, is not a parasitic capacitance. We rely on this capacitance to induce MOS transistor action. The corresponding open circuit transfer function can be obtained from the y-parameter equivalent circuit shown in Fig. l(c) and is given by
Biquadratic
_Yumerical _____________.
Substituting the second-order expressions of Ygd, Ybd, and ysd given in [7] into the above equation yields
10'
1o6
Frequency(Hz)
Fig. 3. Comparison of magnitude and phase of the biquadratic transfer function (solid) and numerical solution (dash) for high-pass 1 with different VGs. Parameters are N, = 1.7 x 10l6C I I - ~ ,to, = 50 nm, V,, = - 1.19 V, L = 100 pm, V,, = 0 V. From left to right, V,, = 2 V, 5 V, and 10 V, respectively.
~ - + t ) l ' z ) and y is the body where 6 = y / ( 2 ( $ ~-~ V,, effect coefficient of the MOS transistor. The parameters cgd, a 2 , and gd are C0,/2, 1/120,, and (1 6)woCOy, respectively. ohlis called the characteristic frequency of the filter, i.e., the comer frequency [ 141 of a high-pass filter. The characteristic frequency of high-pass 1 is thus equal to
+
where at strong inversion WO
=
. _-
L2(1
+ 6)
.
(41
The value of U , at strong inversion approximately equals (2/3)wT, where wT is the intrinsic cutoff frequency of a MOSFET. The characteristic frequency a h 1 can be rewritten as 2 Whl = = 3.3WT. (5) 3
-mu,
The high-frequency gain of the biquadratic function is 1. The Q factor of the filter in (2) is given by QI
= Whla2.
(6)
With zero biased V,, , Q1 equals to (1/ &)( = 0.408). As shown above, the filter operates at frequencies beyond the intrinsic cutoff frequency range. Also, the characteristic frequency of the filter is about three times the intrinsic cutoff frequency and changes with the MOSFET parameters. For a specific technology, the characteristic frequency of the filter could be adjusted by either changing the channel length or varying the gate-source voltage V,, through the straightforward relationship shown in (3) and (4). The characteristic frequency whl increases linearly with V,, - VT and decreases with L2. Figs. 3 and 4 show the magnitude and phase of the biquadratic transfer function (solid) with
Frequency(Hz1
Fig. 4. Comparison of magnitude and phase of the biquadratic transfer function (solid) and numerical solution (dash) for high-pass 1 with different channel lengths. From left to right, the channel length equals 100 j m , 50 pm, and 20 pm, respectively. The other parameters are the same as in Fig. 3 except V,, = 2 V.
different V,, and different channel length L. The characteristic frequency for L = 100 pm, 50 pm, and 20 pm are 3.5 MHz, 14 MHz, and 88 MHz, respectively, with V,, = 2 V. In practice, the high-pass characteristics of a filter can only be maintained in a restricted frequency range. The frequency response of high-pass filter 1 with a buffer and a load will be given in Section 2.3. To ensure the accuracy of the transfer function obtained by the second-order model of a MOSFET, it is compared to the very high frequency numerical model of a MOSFET proposed by Pu and Tsividis [lo]. The model given in [lo] was verified through extensive comparisons to measured results, and to results obtained by simulation of a many-segment device [lo]. The authors of [lo] provided a y-parameter numerical model for MOSFET in strong inversion. The closed-form expression of the y-parameters are obtained for
I IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-I: FUNDAMENTAL THEORY AND APPLICATIONS,VOL. 39, NO. 3, MARCH 1992
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the special cases of V,, = 0 and of the saturation region. We refer to the solution obtained from this model with V,, = 0 as “the numerical solution” in this paper for convenience. The transfer function of the numerical model for high-pass 1 is defined as
TIn --- =vout I+-
vi
= -(1L o x
24w,
+ 6 + 2k,, + 2kj)
Yds
ydd
(7)
(14)
where
= gd = (l
where U, has the same meaning as previously stated. Noticing that the result given by (7)-(9) is the same as the one derived by the uniform R C line method. Comparing to the uniform RC line method, the process of the derivation of the transfer function presented here is simpler and more straightforward. The involved parameters are all standard MOS transistor parameters. The magnitude and phase characteristics of the biquadratic transfer function and the numerical transfer function are compared in Figs. 3 and 4. As can be seen from Figs. 3 and 4, the biquadratic transfer function approximates the numerical mod el very well.
2.2. The Eflects of Parasitic Capacitances When the channel length becomes shorter,’ the overlap capacitance of the gate and the drain CO,,and the drainsubstrate junction capacitance Cdbe should be included in the transfer functions derived in the last subsection. The overlap and junction capacitances are distributed over the resistive n+ material of the source and the drain [4].However, such distributed effects can be neglected if the sheet resistance is much smaller than that of the channel. Hence, the overlap and junction capacitances are considered as lumped elements in this paper. The transfer function of high-pass 1 with parasitic capacitances can be derived from Fig. l(c) and is given by
+ 6)coxo,
(15)
and k,, = C o u / C g d , kj = c b d e / c g d . The parameters b, and b, are l/6w, and 1/120w2,, respectively. Wl,, [l 11. The The overlap capacitance CO,equals CO, value of the junction capacitance Cbde depends to a large extent on the substrate doping concentration, drain geometries, and the biased voltage VDB.For a highly doped substrate, large drain area, and a small channel length, the junction capacitance can dominate the intrinsic capacitances [ 111. The minimum channel length where the parasitic capacitances can be neglected depends on the fabrication process and the geometrical parameters of a MOSFET. A comparison of the third-order transfer function Ti and the second-order transfer function T, derived in the last subsection is shown in Fig. 5 with L = 5 pm, 20 pm, 50 pm. For Fig. 5, it is obvious that the biquadratic function approximates very well the third-order function for L L 20 pm. The third-order transfer functions with k,, + kj = 0, 147 and 2.9 are given in Fig. 6 for L = 5 pm. It is seen from Fig. 6 that the transfer function shift caused by parasitics can no longer be ignored for shorter channel length. In plotting those figures, Canadian Microelectronics Cooperation 3-pm process (CMC3) parameters are used, where G-D overlap capacitance, zero bias bulk junction capacitance, and bulk junction sidewall capacitance are 3 x lo-’’ F/m, 4.4 x lop4 F/mZ, and 4 x lo-’’ F/m, respectively. The overlap capacitances for L = 10 pm and L = 5 pm are approximately 0.17 C gd and 0.1 C g d , respectively. The junction capacitances in Fig. 6 are 1.29 Cgd and 2.69 c g d with two different drain areas (20 pm x 3 pm) and (20 pm x 8 pm), respectively (C,d = COx/2= 3-45X IOp2 PF). When k,, + kj is not negligible, the filter characteristics will shift to the left as shown in Figs. 5 and 6 depending on the value of k,, kj. It is very desirable to relate the frequency shifting quantatively to k,, and kj. Fortunately, this can be achieved approximately. When the condi(1 6/2(k,, kj))) is satisfied, the tion S < 20o,(1 third term in the transfer function is much smaller than the second terms. Hence the third-order transfer function in (10) can be approximated by a second-order transfer function below a certain frequency. Actually, the two third-order terms in the transfer function mainly affect the high frequency gain. The characteristic frequency oil and the Q factor of the approximated biquadratic transfer function by neglecting the third-order terms are given as
+
Substituting the second-order expressions of Y g d , y b d , and Ysd given in [7] into the above equation, yields
’
T‘ =
+
+
A i l s A21s2 A3,S3 BO, B11S 4 1 S 2 & , S 3
+
+
+
(11)
where
A,,
=
B,,
=
-(1 2
=
cox
+ 6 + k,, + kj) + 6 + k,, + kj)
Cgd(l
(12)
‘All distributed MOSFET used in this paper will still be considered as long channel MOSFET in today’s fabrication technology.
+
+ +
= whl
+
1
+ 6 + 2(k0, + kj)
r2
(16)
LI AND EL-MASRY: DlSTRlBUTED hlOSFET
173
C,,, etc. But this effect can be tuned out, fortunately, through voltage control. Some simulation results about tuning are given in the following subsection. The transfer function of the numerical model including the parasitics for high-pass 1 is given by
T----------
g d d m c s c h
-
-1gd
d
m
d
d J Z
m + SCgd(
kou
+ kj)
'
(18) FrequeicyW
Fig. 5 . Comparison of the third-order (solid) and second-order (dash) transfer functions for high-pass 1. From left to right, the channel length equals 50 pm, 20 pm, and 5 pm, respectively. The parameters are N, = 5 X 10'' ~ m - ~to,, = 40 nm, V,, = -1.18 V, VGs = 2 V. and VSB= 0 v.
x al
2. x t-
r
x Frequercy(H2
Fig. 6 . The dependence of {he characteristic frequency shift of high-pass k, = 2.9, 1.47, and 0 . The filter 1 on parasitic capacitances with k , , parameters are the same as in Fig. 5 .
+
Q;
((1 =
Q
i
+ 5)(1 + 6 + 2 k , , + 2 k j ) } l ' * 1 + 6 + k , , + k, p
(17)
where oh,and Q1 are the characteristic frequency and the Q factor of the biquad transfer function obtained for the case ( k , , + k,) = 0. Hence the characteristic frequency and the Q factor of the high-pass filter decreases with the increase of the parasitic capacitances. For example, the characteristic frequencies w i l with k,, k, = 1.47 and 2.9 calculated from (16) are 0 . 5 9 ~and ~ ~0.46whl, respectively. It is seen from Fig. 6 that the estimated shift of the characteristic frequency from (16) is quite accurate. Using (17), the corresponding Q factors of the filters in Fig. 6 are 0.89Ql and 0.75Q,. The degradation of the Q factor with increasing parasitic capacitances can be observed from Fig. 6. Notice that the shift observed in Fig. 6 is not accurately determined before fabrication due to a lack of the exact knowledge of
+
Fig. 7 compares the third-order transfer function (solid) and the numerical solution (dash) for high-pass 1 with L = 10 pm and 5 pm. The junction area for L = 10 pm is (20 pm x 3 pm). The parameter k , , and k j are 0.1 and 0.64, respectively. 2.3. Circuit Simulation Results
In this subsection, simulation results of high-pass filter 1 with buffer and load capacitance are presented. Notice that all the distributed MOSFET's are simulated in SPICE using a many-segment method [9]. CMC3 and CMC4 process parameters are used in the SPICE simulation. First, the distributed MOSFET and its bias circuit shown in Fig. l(b) is simulated on SPICE. As pointed out earlier, the source-follower is bypassed at very high frequencies due to direct feedthrough from the substrate to the gate of the distributed MOSFET. Hence, the high-pass characteristics of the three-transistor circuit will not deteriorate even at frequencies beyond the 3-dB cutoff frequency of the sourcefollower, as shown in Fig. 8. In Fig. 8, the corresponding frequency response of the biquadratic and the numerical transfer functions are also shown for comparison. Good agreement among the three of them is obtained. The complete circuit with buffer and the load [4] is shown in Fig. 9. PMOS source-follower is used as an output buffer to drive the capacitive load. The simulation result of the circuit shown in Fig. 9 with C, = 1 pf is given in Fig. 10. For higher frequency operation, a submicron MOSFET buffer such as the output stage designed in [6] can be used. However, a gain stage may be needed in some applications. To show the tunability of the circuit, worst-case variations of the parasitics are studied. With large variations of all the parasitic capacitances, the control voltage I/ can still tune out all fabrication process tolerances, as shown in Figs. 11 and 12. More information on various automatic tuning techniques can be found in [12]. The distortion of a distributed MOSFET is extensively studied in [13]. For a distributed MOSFET high-pass filter, the distortion decreases with increasing frequency. For example, the second-order and the third-order harmonic distortions for a 0.3-Vp-p input were about - 30 dB and - 54 dB at w = 5w,, and were about -45 dB and -77 dB at w = l o w , [13]. The thermal noise of a distributed MOSFET at very high frequency is studied in [lo]. The equivalent input noise and drain voltage noise of a MOSFET also
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 39, NO. 3, MARCH 1992
0
P
q e,
x 0
1:
FrequencyCIz)
FrequencyMz)
~Biquadratic
Cgdo = 3.18 x lo-'' 3.4 x lO-''F/m.
_Numerical _____________.
F l m , Cj= 4.1 x lo-,
Flm',
and Cjsw=
Fig. 8. The frequency response of the three-transistor circuit shown
Cgdo = 3 X lo-'' F l m , cj = 4.4 X lo-, F / m 2 , and CiSw= 4 x lo-'' F l m . For PMOSFET, the parameters are Nsub= 5 x 10'S/cm3, To,= 50 IIXII, VT = -0.8 V, p, = 250 cm2/ VS, Y8d, = 2.5 x lo-'' F l m , C, = 1.5 x lo-, Flm', and CiSw= 4 x 10- F l m .
Fig. 1 1 . Frequency response of the filter shown in Fig. 9 for different parasitic capacitance values. The ratio k j = Cbde/Cgd equals 0.58, 4.9, and 9.7 with V = 3 V. The other parameters are the same as in Fig. 10.
decrease with increasing frequency. The induced gate noise of a MOSFET increases with the frequency as well. One group of data in [lo] is given here to show the quantitative level of the thermal noises: at o = low,, the equivalent input noise, the drain voltage noise, and induced gate noise are 15 nV/&, 13 nV/&, and 1 PA/&, respectively.
V0.t
Fig. 9.
High-pass filter 1 with a PMOS buffer and a load.
III. HIGH-PASS 2 AND HIGH-PASS 3 Two additional MOSFET high-pass filters are investigated in this section. High-pass 2 was proposed in [4]. In addition, we studied another high-pass configuration, high-pass 3. The schematics and the y-parameter small-signal equivalent circuits for high-pass 2 and high-pass 3 are given in Figs. 13 and 14, respectively.
175
LI A N D EL-MASRY: DISTRIBUTED MOSFET
The corresponding numerical transfer function is T2n
T,, = 1+6'
i
/ Id
FrequencyWz) 1' 0
10'
The biquadratic and numerical transfer function of high-pass 2 is the same as those of high-pass 1 except that the highfrequency gain is 1/(1 + 6) instead of 1. High-Pass 3: Using the same method, the transfer function with zero-biased drain-source voltage for high-pass 3 can be easily derived: Ygd
T3 = Ygd
+ ygb
(21)
+ Y g b + Ybs + Ysd
Substituting the second-order expressions of Y g d , Y g b , and ysd given in [7] into the above equation, we have
Fig. 12. The tunability of the filter for the variations of the parasitic capacitances shown in Fig. 1 1 . The corresponding tuning voltages are V = 3 V, 2.8 V, and 2.5 V.
'quivalent circuit
(20)
T3 =
+ (wh3/(1 + 8)Q)S s2 + ( w h 3 / Q > S 4 3
(22) '
The details of the derivation is given in the Appendix. The characteristic frequency w h 3 , the Q factor, and the high frequency gain are given by the following equations:
+ 6) J 1 + 46 + d 1 + 46 + 62
rnw,(l wh3
=
I
(b)
Fig. 13. Schematics for (a) high-pass 2 and (b) high-pass 3 .
3. I . Neglecting Parasitic Effects High-Pass 2: The transfer function with zero biased drain-source voltage for high-pass 2 is derived as m
1 1 r, = -
(23 1
(1 + 6 ) &
Q3=
--
Ybs,
1 + 36 + 46 + 6, With small 6 values, w h 3 = mu,,Q = l / & ,
K =
1
and K = 1. The Q factor has a maximum value of 0.5 at 6 = 1. The variation range of the Q factor with 6 is 0.4 to 0.5. The parameter 6 affects very slightly the value of w h 3 . Similar to high-pass 2, the high frequency gain decreases with the increase of 6. The corresponding numerical solution for high-pass 3 is given by
1+6
Ygg
T= Ygg
+ ygs
+ 2Ygs + Ydd
(26)
where 1 Y g s = - -( Y d d + y d s ) 1+6 1 Y g g = -(SWLC,, - 2 Y g s ) 1+6
Vin
(b)
Fig. 14.
Y-parameter small-signal equivalent circuits for (a) high-pass 2 and (b) high-pass 3.
and yds and y d d are defined in (8) and (9). Fig. 15 compares the magnitude and phase characteristics of high-pass 3 with the biquadratic transfer function (solid) and numerical solution (dash). Discussion: It can be seen that the main difference of the three high-pass filters is the high frequency gain. The high frequency gains of high-pass 1, high-pass 2, and high-pass 3 are 1 , 1/(1 + 6), and (1 36)/(1 46 + S2), respectively. For small values of 6, the high frequency gains of high-pass
+
+
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176
I
=I
Frequency(Hz.1
Fig. 15. Comparison of magnitude and phase of the biquadratic transfer function (solid) and numerical solution (dash) for high-pass 3. From left to right, the channel length equals 50 pm and 20 pm, respectively. , = 1.34 fF pm-', The parameters are N, = 2 x lOI4 ~ m - ~C& V,, = -0.88 V, W = 20 pm, V,, = 2 V, V,, = 5 V.
'e
0-
2 and high-pass 3 are very close to 1. The value of 6 decreases with the increase of the applied voltage V,,. Reducing the doping density of the substrate and the gate oxidation thickness will also result in a decrease of the value of 6. Unfortunately, the process parameters are specified in the fabrication for most cases. Hence, the high frequency gains of high-pass 2 and high-pass 3 can only be adjusted by V,,. For a typical NMOS process, with the doping range of NA = 2 x lo2 to 6 x lo2 p m P 3 [9], the value of 6 is around lo-'. For a CMOS process, the typical value of 6 could be about 0.1. For a highly doped substrate process, for example, the CMC3 process, 6, is equal to 0.59 with V,, = 0 and 0.23 with V,, = 5 V. Hence, the high frequency gain may be too small for a highly doped substrate process with zero-biased V,,. The magnitudes of the three high-pass filters with 6 = 0.23 and 0.59 are shown in Fig. 16. The high frequency gains of high-passes 1, 2, and 3 with V,, = 5 V and 0 V are 1, 0.81, 0.86 and 1, 0.63, 0.75, respectively. 3.2. The Eflects of Parasitic Capacitances High-Pass Filter 2: The transfer function with parasitic capacitances for high-pass 2 can be derived from Fig. 13@) and is given by
Ti =
+ Ybd A,,s + A2,s2 + A3,s3 Bo2 B,,s + B22s2+ &S3
+
(29)
where all the coefficients are listed in the Appendix. The corresponding numerical transfer function including parasitics is
T'--%ut 2n -
vi"
-
6 = 0.59
High-pass 3
FrequencyWz)
(b)
Fig. 16. Comparison of the magnitudes of the biquadratic transfer function for high-pass 1 (solid), high-pass 2 (dash), and high-pass 3 (chain-dash) with (a) 6 = 0.23 and @) 6 = 0.59. The other parameters are N, = 1.7 x 10l6 ~ m - to, ~ , = 50 nm, V,, = - 1.19 V, L = 50 pm, V,, = 2 V.
The characteristic frequency wh2 and the Q factor Q; of the transfer function with parasitics for high-pass 2 are the same as those of high-pass 1, as given in (16) and (17). High-Pass Filter 3: Using the same method, the transfer function with parasitic capacitances for high-pass 3 can be derived:
ygd - "ou + Ysd - s(cou + cbde>
Ygd
-
High-pass 1 High-pass 2 _________-------
( l / l + 6 ) ( Y d s + Y d d ) + SCgdkou Ydd + "gd( k m + k j )
where y&, and yds are defined in (8) and (9).
-
+ A23s2 + A33s3 + B,,s + B 2 3 ~+2 B3,s3
A,,, B,
where all the coefficients are defined in the Appendix. Notice that kj is equal to Cbse/C,, for high-pass 3. There is one additional term, 26/(1 6) in the coefficients A23 and B23 of high-pass 3 comparing to high-pass 2. The rest of the terms of high-pass 3 are the same as those of high-pass 2.
+
(30)
(31)
LI AND EL-MASRY: DISTRIBUTED MOSFET
177
given in [4] for a modern fabrication process, the high frequency gain of high-pass 2 and high-pass 3 is 0.25. High-pass 2 ...___...._.____ However, the parasitic capacitances will not affect the high High-pass 3 frequency gain of high-pass 1. The high frequency gain of high-pass 1 becomes 1 due to direct capacitive feedthrough to the output. But, the high frequency gain of high-pass 2 and high-pass 3 depends on the extrinsic capacitance ratio CO,/ ( C O ,+ Cbde).Hence, high-pass 1 is superior compared to high-pass 2 and high-pass 3. Discussion: In plotting the curves in this paper, the source-drain diffusion resistances have been calculated based on the formula given in [ 111. Calculation showed that these resistances are negligible. Hence, the effect of parasitic resistances is not included in the transfer functions. The parasitic Frequencflz) resistances depend greatly on the resistivity of the source and drain regions, their geometry, and the way they are conFig. 17. Comparison of the third-order transfer function of high-pass 1 (solid), 2 (dash), and 3 (chain-dash) with L = 5 pm, k,, = 0.2 and tacted, etc. No general rules can be given for the frequency kj = 1.27. The other parameters are the same as in Fig. 15. where such effects become important [9]. Notice that the suggested frequency limit of validity The corresponding numerical solution for high-pass 3 is of the second-order model of a MOSFET in [7] is 40,. The second-order model was used in this paper to given by predict the high-pass characteristics at frequencies beyond this limit. However, the suggested upper frequency is only a rough indication of the region within which the model will perform satisfactorily in most cases. The actual upper frewhere quency limit of validity depends on the specific situation. In 1 our cases, the high frequency gain of high-pass 1 becomes 1 Ygs = (Ydd + Yds) (33) due to direct capacitive feedthrough to the output anyhow. The high frequency gain of high-pass 2 and high-pass 3 only /(CO” Cbd,). depends on the extrinsic capacitance ratio CO, (34) Hence, a satisfactory result has been obtained from the and yds and Y d d are defined in (8) and (9). The characteristic second-order model in all frequency range. It is worth menfrequency shift and the Q factor of high-pass 3 with parasitics tioning that the first-order model in [7] is not able to predict the characteristics of the high-pass filters presented in the are given by the following equations:
I+s
+
0L3
= wh3
Q; = Q3
1 + 46 + 62 + 46 + 62 + 2(1 + 6 ) ( k , , + kj) { ( 1 + 46 + 6 2 ) [ 1 + 46 + h2 + 2(1 + 6 ) ( k , , + k j ) ] } 1 ’ 2 ( 1 + 6 ) ( 1 + 6 + k,, + k i )
I
1
For small value of 6, n e have
Q’
{1
- -
3 -
+ 2( k,, + kj)}’/* 1 + k,, + k j
The Diflerence Bet ween the Three High-Pass Filters with Parasitics Includt?d: The difference between the three high-pass filters with parasitic capacitances included still focuses on the high frequency gain. The high frequency gain of high-pass 2 and high-pass 3 is C,,,/(C,, + C,,,) instead of 1 for high-pass 1. High-pass 2 and high-pass 3 will not exhibit high-pass characteristics for large values of the junction capacitance, as shown in Fig. 17. Using typical values of CO,= (0.2 fF/pm) x W and Cbde= (0.6 fF/pm) x W
i
(35)
(36)
paper. The upper frequency limit of the first-order m ode1 is U,. However, the characteristic frequency of the high-pass filter s is about 3.30,. The frequency region from U, to 4 0 , is very critical for the high-pass filters. Hence, the high-pass characteristics canno t be predicted accurately using the first-order model. Notice that all distributed MOSFET’s in this paper are long channel devices. A submicron MOS device as a distributed element is not applicable in the settings of this paper because of the following reasons. It is known that the proposed distibuted filter topologies are likely to be used in conjunction with lumped active circuits. Consider the case that a distributed MOSFET filter is connected to an output stage, for example, the circuit shown in Fig. 9. The transistors of the output stage are designed to operate as lumpedparameter devices, below their intrinsic cutoff frequency. However, the distributed MOSFET works beyond its cutoff
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 39, NO. 3, MARCH 1992
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frequency. To match the speed, the channel length of a distributed MOSFET must be comparably larger than those in the output stage, which can be of minimum length. Hence, the operating frequency required to MOSFET’s functioning as lumped elements would be too high to realize if a submicron distributed MOSFET is used as a high-pass filter.
4 2
= =
B32
cgd[(l cox
-(1 24 U,
+ &)a2 +
(kou
+ kj)bI]
+ 6 + 2k0, + 2k,)
= Cgdb2(kou
+ kj)
Cox(kou
=
(45)
+ kj)
240 U’,
(46)
IV. CONCLUSION This paper presents a new method for analyzing distributed MOSFET filters. The analysis method is verified using SPICE simulation and the very high frequency model of a MOSFET in [lo]. Three schemes of MOSFET configurations functioning as distributed high-pass filters are analyzed to demonstrate the new method and to illustrate the effects of parasitic capacitances. Without parasitic capacitances, the transfer functions of the filters are of biquadratic form using the new method. The characteristic frequency of the filter is around three times the intrinsic cutoff frequency of a MOS transistor. When the junction capacitance of a MOSFET is large, parasitic capacitances are no longer negligible. The transfer functions then all become third order. It is found that one high-pass configuration (high-pass filter 1) is superior to other two. It maintains the high-pass characteristics regardless of the effects of parasitic capacitances. APPENDIX
=
Coxko,
Cgdb2ko,= 240 U’,
+ (1 + 6 ) c , d s
-k
+6
C,,U2(1
26/(1
(49)
26 1+6+ 24w0 1+6
--(
cox
+2kOu+ 2kj
+ C,,a2(l + 26/(1 + 6))s2
cs, gd
A,,
-
In deriving the transfer function of high-pass 3 without parasitic capacitances, from (21)’ we have:
-
26 24 w ,
(52)
(53)
+ 6))s2 ACKNOWLEDGMENT
-
K: (Uh3/(1 6)Q)s s 2 +( U h 3 / Q ) s + w ’ , 3 .
(39)
The coefficients of the transfer functions for the high-pass 2 and high-pass 3 with parasitic capacitances are
A12
=
A22 = -
c,& + ko,)
cox
= -(I
2
+ kou)
(40)
+ kOUbl)
C&2
+ 2k0,)
cox
- -(1
24w,
(42)
+ 6)Coxw0 B,, = Cgd(l + 6 + k,, + k j )
Bm
= gd =
cox
= -(1
2
(1
+ 6 + k,” + kj)
(43)
The authors would like to acknowledge Prof. Y. P. Tsividis for his constructive suggestions. We also thank the reviewers for their valuable comments.
REFERENCES [l] W. Li and E. I. El-Masry, “Biquadratic high-pass and low-pass single-MOSFET filters,” 1991 ISCAS., vol. 3, pp. 1753-1756. [2] J. Khoury, Y. Tsividis, and M. Banu, “Use of transistor as a tunable distributed RC filter element,” Electron. Lett., vol. 20, pp. 187-188, Feb. 1984. [3] Y. Tsividis, “Minimal transistor-only micropower integrated VHF active filter,” Electron. Lett., vol. 23, pp. 771-778, July 1987. [4] L.-J. Pu and Y. Tsividis, “Transistor-only frequency selective circuits,” IEEE J. Solid-state Circuits, vol. 25, pp. 821-832, 1990. [5] Y. Tsividis, “A transistor-in-the-boxpuzzle,” Circuit and Devices Mag., vol. 4, p. 117, Apr. 1984. [6] R. P. Jindal, “Gigahertz band high-gain low-noise AGC amplifiers in fine line NMOS,” IEEE J. Solid-State Circuits, vol. SC-22, pp. 512-521, 1987. [7] M. Bagheri and Y. Tsividis, “A small signal dc-to-high-frequency nonquasistatic model for the four-terminal MOSFET valid in all regions of operation,” IEEE Trans. Electron Devices, vol. ED-32, pp. 1283-1291, NOV.1985. [8] R. P. Jindal, “Low-pass distributed RC filter using an MOS transistor with near zero phase shift at high frequencies,” IEEE Trans. Circuits Syst., vol. 36, pp. 1119-1123, Aug. 1989. 191 Y. Tsividis, Operation and Modeling of the MOS Transistor. New York: McGraw-Hill, 1987.
LI AND EL-MASRY: DISTRIBUTED MOSFET
[lo] L. J . Pu and Y . Tsividir., “Small-signal parameters and thermal noise of the four-terminal MOSFET at very high frequencies,” Solid-State Electronics, vol. 33, pp. 513-521, May 1990. [l I] M. Bagheri, “Four-terminal MOSFET modeling including nonquasistatic and moderate inversion effects,” Ph.D. dissertation, Columbia Univ. [I21 Y . Tsividis, M. Banu, and J. Khoury, “Continuous-time MOSFET-C filters in VLSI,” IEEE Trans. Circuits Syst., vol. CAS-33, pp. 125-140, Feb. 1986. [13] L. J. Pu and Y . Tsividis, “Harmonic distortion of the four-terminal MOSFET in non-quasistatic operation,” Proc. Inst. Elec. Eng., pt. G, vol. 137, pp. 325-332, May 1990. [14] S. Soclof, Design and .4pplications of Analog Integrated Circuits. Englewood Cliffs, NJ: Prentice-Hall, 1991.
Wei Li received the B.S. degree in applied physics in 1982 from Northwestern Institute of Telecommunication, China, and the M.S. degree in electrical engineering in 1986 from the University of Pittsburgh. From 1987 to 1988, she was a part-time research assistant at the Center of Robotics in Microelectronics, University of California, Santa Barbara. She is currently completing the Ph.D. degree in electrical engineering at the Technical University of Nova Scotia, Canada. Her current research interests are analog and digital IC design, signal processing, device physics and modeling, and circulit and device simulation CAD.
179
Ezz 1. El-Masry (M’78-SM’83) received the B.Sc. (honors) degree in electrophysics and the M.Sc. degree in electrical engineering from Alexandria University, Egypt in 1967 and 1972, respectively, and the Ph D degree in electrical engineering from the University of Manitoba, Winnipeg, Canada, in 1977 He was a member of the scientific staff at the National Research Council of Cahada in Ottawa, Canada. In 1978 he joined the Department of Electrical Engineering and the Coordinated Science Laboratory at the University of Illinois at Urbana, I11 In 1983 he joined the Department of Electrical Engineering at the Technical University of Nova Scotia, Halifax, NS, Canada, where he is currently a Professor. In 19891990 he was a visiting professor at Kuwait University. He is the founder and president of the EEC Engineering Consultant in Dartmouth, NS, Canada. His research interest are in the areas switched-capacitor artificial neural networks, high-speed analog filters, and analog VLSI. Dr. El-Masry is a member of Canadian Network of Centres of Excellent of Microelectronics (Micronet). He is a member of the steering committee of the Midwest Symposium on Circuits and Systems. He was the chairman and organizer of technical sessions in the 1984 and 1985 Midwest Symposia on Circuits and Systems, chairman of the technical program corrrrmttee of the 1984 IEEE International Conference on System, Man and Cybernetics, chairman of technical sessions of the 1984, 1987, 1988, 1989, and 1991 IEEE International Conferences on Circuits and Systems, and a member of the technical program committee of the 1981 IEEE International Conference on Circuits and Systems. He received Myril B Reed Best Paper Awards presented at the 27th and the 28th Midwest Symposia on Circuits and Systems in 1985 and 1986
