Discussion

In this chapter several microwave active filter techniques employing the active inductor and the active resonator have been reviewed. Conventionally these techniques rely on the active transistor with low intrinsic capacitance (C_gs), high quality inductively feedback network, good transconductance efficiency, or good matching properties. To make monolithic CMOS active filters without these restrictions, an active CCS TL based approach had been chosen for its favorable lossless guiding characteristics and low complexity so that general filter synthesis methods could be used. However, the preliminary experiment was failed for instability issues at 10.1 MHz. Therefore the design philosophy must apply adequate loss compensation in order to make the active filter stable through the entire frequency spectrum. This strategy will be explored in Chapter 4 in view of the filter’s architecture.

CHAPTER 4

Miniaturized C-Band Active Bandpass Filter

This chapter presents a C-Band monolithic active bandpass filter based on Q-enhanced half-wavelength resonators in a standard CMOS 0.18 µm technology.

The quality factor of the complementary-conducting-strips transmission line (CCS TL) based half-wavelength resonator is reported in Section 4.1. Section 4.2 describes the design philosophy of the composite Q-enhanced resonator incorporating the cross-coupled pair circuit with the CCS-TLs based half-wavelength resonator. Within this novel architecture, the loss-composition mechanism could be well controlled both in architecture level and circuitry level. The two operation modes of the Q-enhanced resonator are theoretically investigated. Section 4.3 presents the realization of the second-order prototype bandpas filter based on the proposed Q-enhanced resonator in great detail. When consumes 3.0 mA from a 1.8 V supply, the active filter demonstrates a 2.2-dB insertion loss. Theoretically analyzed two-port scattering parameters are in good agreements with the measured results. The trend of the active bandpass filter with a 0.56-dB transmission gain is also theoretical and experimentally investigated. For this particular case, however, the reflection coefficient is greater than 0 dB from 6.5 GHz to 7.9 GHz. Based on a set of 50-Ω terminations, the noise and nonlinear properties of the prototype filter with a 2.2-dB insertion loss are further analyzed in Section 4.4 and 4.5. The stability analysis of the proposed active filter is performed in Section 4.6. Section 4.7 compares the filter performance with other published works and indicates the direction for further improvements.

4.1 CCS TL Half-Wavelength Resonator

In view of miniaturizing the size of complementary-conducting-strips transmission line (CCS TL) based half-wavelength resonator, the meandered CCS TL of the largest slow wave factor (SWF) should be employed. But there will be both DC and microwave signals carried in the top layer strip of the meandered CCS TL. Therefore the one with equal W and S of 30 µm is the best candidate for lowering the power dissipation introduced by the DC resistance. Base on the studies performed in Section 2.2, one can quickly estimate the physical length of a half-wavelength resonator by using CCS unit cells of W = S = 30 µm, P = 44.0 µm, and Wh= 40 µm at 6.0 GHz to be 12,480 µm and such meandered transmission line can be compacted in an chip area of 748 x 748 µm². In contract, if the similar meandered microstip of a 30-µm width is applied, there will be an additional length requirement of 1.42 mm corresponding to a 12.1 % increase in the chip area. Though the loss property of meander microstrip is about 1.5 dB lower than the meandered CCS TL for a half-wavelength resonator at 6.0 GHz. But it would be clearer in Section 4.2 that this impediment could be easily overcome by applying negative resistance circuit.

However, for example, the meandered CCS TL of W=30 µm and S = 15 µm posses a better loss characteristic, better slow property, and modest average width in the top layer strip compared to the one of W = S = 30 µm. With the CCS TL of unequal W and S, a passive half-wavelength resonator could be further optimized in respect to the DC-resistance, high-frequency loss, and chip area. But for simplicity and for the same reason about the loss issue, the meandered CCS TL of S = W = 30 µm is employed for designing the prototype active bandpass filter.

For clearness, the guiding characteristics of CCS TL of S = W = 30 µm from 1 GHz to 8 GHz is derived by using the same software-based analysis method described in Chapter 2. Figure 4.1 illustrates the extracted results of the particular CCS-TL design example. From 1.0 GHz to 8.0 GHz, the real part of the characteristics impedance (Z_c), which is the solid line plotted in Fig. 4.1(a), nearly keeps at a constant value of 34.2 Ω.

The imaginary part of Zc is capacitive, ranging from -11.7 Ω to -2.04 Ω. The normalized phase constant shown in solid line in Fig. 4.1(b) illustrates the value of 2.0 at the desired operating frequency. The normalized attenuation constant, which is plotted by the dotted symbol in Fig. 4.1(b), however, shows relatively high loss aspect of the transmission line. In the low frequency limit (1 GHz), the metal thickness employed in the CCS-TL is smaller than the skin depth, thus we observe larger attenuation losses. Figure 4.2 plots the Q-factor of CCS-TL against frequency, showing 2.19, 2.94, and 3.40 at 3.0GHz, 5.0GHz, and 6.53GHz, respectively.

Therefore the Q-factors our resonator design are comparable but smaller than those of inductor-based design in [18-20, 22-24].

(a)

(b)

Fig. 4.1 Guiding characteristics of the meandered CMOS CCS TL with W = S = 30 µm, P = 44 µm, and Wh = 40 µm from 1 to 8 GHz. (a) Complex characteristic impedance. (b) Normalized complex propagation constant.

Fig. 4.2 The Q-factor of the CCS TL-based half-wavelength resonator from 1 to 8 GHz.

4.2 Q-Enhanced Monolithic Half-Wavelength Resonator

Figure 4.3 illustrated the concept of a Q-enhanced complementary-conducting- strips (CCS) half-wavelength resonator. A cross-coupled pair, which consists of two identical NMOS transistors, is integrated into a passive CCS-TL based half-wavelength resonator. The Drain terminal of N1 is directly connected to the Gate terminal of N2 and vise versa. Two transistors are biased at the same DC potential (VG), and the Drain terminals of both N1 and N2 are directly loaded with CCS half-wavelength resonator, forming a new composite resonator.

CCS λ

/2 Resonator

A B

N1 N2

V

V

CCS λ

/2 Resonator

A B

N1 N2

V

V

Fig. 4.3 Q-enhanced CCS half-wavelength resonator incorporating a NMOS cross-coupled pair.

Applying to conventional filter synthesis flow, the active resonator will be excited single-endedly, not differentially, both common-mode and differential-mode signals will excite in the active resonator structure. Part (a) and (b) of Fig. 4.4 illustrate the equivalent circuits for differential-mode and common-mode excitations, respectively.

When a differential-mode signal transmits into a cross-coupled NMOS transistors pair and establishes a positive feedback, a virtual ground is formed at the symmetric plane rendering a negative differential resistance –Rd in Fig. 4.4(a) with magnitude approximately equal to the inverse of transconductance of the cross-coupled pair [73].

On the other hand, the capacitance across the resonator is approximately half of the combined capacitance (Cgs+Cgd).

Since the potentials on the Drain and Gate terminals of the NMOS are equal under a common-mode excitation, the NMOS acts as a Gate-Drain-connected diode.

Therefore two parallel RC networks are loaded with both sides of the half-wavelength resonator. The shunt resistance R_c shown in Fig. 4.4(b) represents the small signal resistive loss of the transistor operated in the saturation region. To make proper operation of active bandpass filter, the differential-mode must prevail over the common-mode in the passband. Since the cross-coupled pair can amplify the differential-mode signal and attenuate the common-mode signal, such circuit characteristic can increase the common-mode rejection of the proposed Q-enhanced resonator, and relax the issue on symmetrical layout of the resonator during the filter integration.

±

Fig. 4.4 Small signal analyses of the Q-enhanced half-wavelength resonator. (a) Differential-mode analysis. (b) Common-mode analysis.

Then the complex input impedance under differential-mode excitation was theoretically investigated by using the software, Agilent^TM ADS2004A. Through the analysis, the length and width of the two transistors were set at 0.18 µm and 80 µm, respectively. And V_G was isolated from the differential RF signal by RF-choke. The results illustrate that the value of Cd and –Rd were nearly constant from 1.0 GHz to 8.0 GHz, revealing a broadband characteristic of the equivalent active RC circuit. And the total equivalent resistance (Requ) of the differentially driven active resonator can be expressed by

d L

L d

equ R R

R R R

−

⋅

=− (4)

where RL represents the loss of the CCS half-wavelength resonator. Because the value of the frequency-dependent R_L increases with increasing frequency, the active resonator tends to become more stable at frequency higher than the resonant frequency. Furthermore, the value of –R_d is inversely proportional to the Drain current of the NMOS transistors [73]. Thus, as shown in Fig. 4.5, V_G can be applied to adjust proper negative resistance for realizing a stable half-wavelength resonator.

Fig. 4.5. Differential input impedance of a 0.18 µm NMOS cross-coupled pair with length of 0.18 µm and width of 80.0 µm.

The inset in Fig. 4.6 depicts the schematic for extracting the unloaded Q-factor of the active half-wavelength resonator shown in Fig. 4.3. Two tiny capacitors of 0.01 fF formed the electromagnetic coupling between the resonator and loads. Clearly the excitation was single-endedly. The size of the NMOS transistor was the same as that reported in the Fig. 4.6, and the half-wavelength resonator was realized by using the meandered complementary-conducting-strips transmission line (CCS-TL) reported in the Section II.A. As the value of RL of the CCS half-wavelength resonator and –Rd of the cross-coupled pair biased at 557 mV are 298.4 Ω and -301.34 Ω at 6.53 GHz, respectively. Therefore, according to (1), Fig. 4.6 illustrates a stable active half-wavelength resonator.

The extracted Q-factors shown in Fig. 4.6 follow the definition of the unloaded Q-factor in [74]. Moreover, the magnitudes of the transducer gain of the weakly coupled active resonator are also illustrated in Fig. 4.6. The Q-factor was only 3.40 for the passive CCS half-wavelength resonator. With the active Q-enhanced circuit biased at 525 mV, 538 mV, 549 mV, and 557 mV, the enhanced Q-factors were 9, 15, 39, and 84, respectively. Notably, the resonant frequency of the Q-enhanced resonator was slightly shifted from 6.633 GHz to 6.531 GHz when VG was increased. Such frequency drift was caused by the increase of Cd shown in Fig. 4.5.

CCS λg/2

Resonator

P

P

Resonator

P

P

Resonator

P

P

Fig. 4.6 Unloaded Q-factor of Q-enhanced half-wavelength resonator incorporating a 0.18 µm NMOS cross-coupled pair.

4.3 CMOS Transmission-Line based Active Bandpass Filter

Figure 4.7 shows the complete schematic of a second-order bandpass filter (BPF) incorporating the Q-enhanced half-wavelength resonators [29-30]. The J-inverters were realized by series capacitors C1, C2, and C3.The design procedure of the BPF is well documented in [74]. In this practical example, fc of the BPF was located at 6.02 GHz, and BW was 1.0 GHz with ripple of 0.2 dB. The order of the BPF was two and the reference impedances of two terminals (P₁ and P₂) were 50 Ω. The biasing and tuning networks controlled by V_tun provided biasing currents for the NMOS cross-coupled pairs. And these networks were isolated from the CCS-TL resonators by the on-chip spiral inductors as shown in the top of Fig. 4.8. Figure 4.8 also illustrates the die photo of the prototype filter in Fig. 4.7.

The entire active BPF, including the complementary- conducting-strip transmission lines (CCS-TLs), capacitors, inductors, active networks, and pads were fully integrated in a chip area of 1230 µm x 880 µm. The capacitor was realized with the so-called interdigital metal-oxide-metal (MoM) capacitors of top-three metal layers.

In the realizations, C₁ was 380 fF with an area of 45.9 µm x 79.8 µm, and C2 was 220 fF with an area of 41.9 µm x 52.8 µm, respectively. Additionally, the inductance of the on-chip spiral inductors was about 3.0 nH occupied an area of 251 µm x 247 µm.

Fig. 4.7 Second-order CMOS transmission-line based bandpass filter.

Fig. 4.8 Die photo of the prototype bandpass filter in Fig. 4.7.

The small-signal experiments were performed after the on-wafer short-open-load-through (SOLT) procedures had been conducted by the vector network analyzer (VNA), Agilent^TM E5091A. In the measurements, the prototype shown in Fig. 4.7 was biased by a supplying voltage (VCC) of 1.8V with a current consumption of 3.0 mA. The value of V_tun and the power level of input signals were set at 1.0V and -20dBm, respectively. Additionally, the measured result was compared with simulations performed by Agilent^TM ADS2004A. Before the simulation, all the passive components including capacitors, inductors, and CCS-TL were characterized by Ansoft HFSS^TM. The BSIM3 V3.2.4 based RF models used for active devices were provided by the foundry. Figure 4.9(a) shows the comparisons from 3.0 GHz to 8.0 GHz, revealing good agreements between the simulated and measured data. The slight mismatch shows the capacitive coupling between the two Q-enhanced half-wavelength resonators were well controlled through the J-inverter, C2, and parasitic coupling through the lossy substrate was not server owing to the good electromagnetic shield from the meshed ground plane of CCS TL. On the other words, the CCS-TL can effectively confine the electromagnetic propagations and eliminate the un-wanted coupling of the adjacent signal lines in the compact layout.

The measured results of two-port scattering parameters based on the 50 Ω-system lead the following observations. The center frequency of the second-order BPF is 6.02 GHz, and the insertion-loss is about 2.2 dB from 5.38 GHz to 6.65 GHz. The bandwidth is about 1.14 GHz (5.26 GHz to 6.40 GHz) with a return-loss of 7.64 dB.

Two reflection zeros are identified at 5.47 GHz and 6.20 GHz. Additionally, the prototype can reject the low-side signal about 28.18 dB at 4.0 GHz and the high-side signal about 18.33 dB at 8.0 GHz. The superiors-mode of the prototype, which is observed in Fig. 4.9(b), is suppressed about 16.67 dB at 15.25 GHz. The unobvious

superiors-mode reflects that fact that the loss of the composite resonator is not compensated at the corresponding frequency. In other words, for the boundary condition set by the CCS-TL resonator at 15.25 GHz is unable to excite the cross-coupled circuit to generate differential negative resistance for loss compensation.

Based on the same measurement setting with Vtun set at 1.2 volt, as illustrate in Fig.

4.10(a), the center frequency of the prototype bandpass filter is 5.97 GHz. The passband gain is about 0.561 dB from 5.38 GHz to 6.56 GHz. The return-loss is 9.55 dB with a bandwidth of 870 MHz, from 5.5 GHz to 6.37 GHz. The two reflection zeros are identified at 5.47 GHz and 6.125 GHz which almost the same as those observed when Vtun was set at 1.0 volt. Besides, the stopband rejections also remain the same, 27.95 dB at 4.0 GHz and 18.24 dB at 8.0 GHz, respectively. Fig. 4.10(b) depicts the corresponding superiors-mode suppression is about 20.31 dB at 15.8 GHz.

The current consumption increases slightly from 3.0 to 4.0 mA. In summary, the center frequency, 3-dB frequency, and stopband rejections are almost insensitive to the changes of tuning voltage, V_tun. Thus, the passband gain of the prototype bandpass filter could be controlled independent form the other filter characteristics.

Comparing the measured and simulate results when V_tun set at 1.2 volts, the simulated passband gain is a little bit larger than the measured one at the high side of passband edge. This could due to the insufficiency of the circuit model used for emulating the characteristics of the active devices especially at resonance frequency.

Moreover, the measured reflection coefficient is larger than 0 dB from 6.65 to 7.45 GHz which is also observed in the simulated result, from 6.5 to 7.9 GHz. This phenomenon could introduce potentially instabilities and a further analysis would be performed in Section 4.6.

(a)

(b)

Fig. 4.9 Comparison of measured and simulated transmission and reflection characteristics of the prototype active bandpass filter when Vtun set at 1.0 volt. (a) 3 to 8 GHz. (b) DC to 20 GHz.

(a)

(b)

Fig. 4.10 Comparison of measured and simulated transmission and reflection characteristics of the prototype active bandpass filter when Vtun set at 1.25 volt. (a) 3 to 8 GHz. (b) DC to 20 GHz.

4.4 Nonlinear Characteristics

The nonlinear characteristics of the prototype with Vtun equal to 1.0 volt had also been investigated by measuring the input third-order intermodulation point (IIP3) and the 1-dB compression point (P1dB) when the. For the measurement of P1dB, the signal generator, Agilent^TM E8267D, provided an input continuous wave (CW) at 6.02 GHz, and the spectrum analyzer, Agilent^TM E4440A, was applied to observe the output signals of the prototype. For the measurement of IIP3, two signal generators were applied to generate two fundamental frequencies of f₁ and f₂ equal to 5.795 GHz and 5.805 GHz, respectively. Before performing the measurements, the testing system which includes the connectors and cables were calibrated. The measured and simulated results, as shown in part (a) and (b) of Fig. 4.11 indicate the measured input power levels for P_1dB and IIP₃ are -15.2 and -9.6 dBm. Besides the simulated values are -17.8 dBm and -10.69 dBm revealing an average difference of less than 1.8 dB.

To investigate the IIP3characteristics of passband intermodulation distortion (IM3) caused by stopband signals, the same circuit simulation scheme was adopted. For both the f1 and f2 signals originating from upper stopband, f1 was set at 7.5 GHz and f2was swept for 8.5 to 9.7 GHz. Therefore the resultant IM₃ frequency (2f₁-f₂) ranged from 5.3 to 6.5 GHz within the passband of the prototype filter. Similarly, for both signals originating from lower stopband, f₂ was set at 7.5 GHz and f₁was swept for 4.7 to 3.5 GHz, respectively. The simulated IIP3 caused by upper and lower stopband signals are illustrated in Fig. 4.12(a) and (b). As expected, the trends of both cases illustrate that the interfering signals closer to the passband would introduce a larger intermodulation products with a lower value of IIP3. The minimum values are -7.71 dBm and -6.6 dBm for the upper and lower cases and are both larger than the one introduced by passband f1and f2signals. Further increase the distance between f1and f2signals would

result in a higher IIP₃ value. The highest values are -2.23 dBm and -0.86 dBm for the upper and lower cases. Since the stopband rejection is getting larger when f1or f2

signal is farther away from the passband, therefore the generated intermodulation products would become smaller resulting a higher value of IIP3 as well.

(a)

(b)

Fig. 4.11 Nonlinear characteristics of the active bandpass filter prototype. (a) 1-dB compression point measurement of f0 equal to 5.8 GHz (b) Measured third-order intermodulation distortion of f1 and f2 equal to 5.795 GHz and 5.805 GHz, respectively.

(a)

(b)

Fig. 4.12 Input third-order intermodulation intercept point (IIP3) characteristics when passband intermodulation distortion (IM3) cause by signals from (a) upper stopband with f1 fixed at 7.5 GHz, and (b) lower stopband with f2 fixed at 5 GHz.

4.5 Noise Analyses

In this section, the passband noise figure of the prototype active bandpass filter incorporating cross-coupled pair circuit was investigated. An equivalent noisy two port network and analytic expression relating the input referred noise figure are presented and validated. Then the effects of device sizes and operation conditions on the filter noise performance were analyzed as well. Finally a design trade off curve was derived and provides physical explanations in attending minimum noise-figure values of the proposed active filter.

4.5.1 Equivalent Noise Two Port Network

Experimental results in Fig. 4.9 indicate that the prototype filter behaves like a passive one with an insertion loss of 2.2dB. According to the text-book definition, the noise figure of a passive two-port network is equivalent to the inverse of its available power gain [75]. However, the proposed bandpass filter, as depicted in Fig. 4.7, comprises of complementary-conducting-strip transmission lines (CCS-TL) and differential NMOS cross-coupled pairs. The cross-coupled pairs not only provide negative resistance to enhance the quality factor (Q-factor) of the resonators, but also produce the noise simultaneously. Therefore, the noise contributions from the transistors need to be incorporated into the noise figure calculation of the prototype filter. The noise characteristics of a NMOS cross-coupled pair had been well documented in [76-77]. The differential output noise current spectral density of a NMOS cross-coupled pair is equivalent to the summation of thermal noise generated in the channels of two NMOS transistors [77]. Furthermore, the channel noise of a

Experimental results in Fig. 4.9 indicate that the prototype filter behaves like a passive one with an insertion loss of 2.2dB. According to the text-book definition, the noise figure of a passive two-port network is equivalent to the inverse of its available power gain [75]. However, the proposed bandpass filter, as depicted in Fig. 4.7, comprises of complementary-conducting-strip transmission lines (CCS-TL) and differential NMOS cross-coupled pairs. The cross-coupled pairs not only provide negative resistance to enhance the quality factor (Q-factor) of the resonators, but also produce the noise simultaneously. Therefore, the noise contributions from the transistors need to be incorporated into the noise figure calculation of the prototype filter. The noise characteristics of a NMOS cross-coupled pair had been well documented in [76-77]. The differential output noise current spectral density of a NMOS cross-coupled pair is equivalent to the summation of thermal noise generated in the channels of two NMOS transistors [77]. Furthermore, the channel noise of a