Q-enhanced LC-based active BPFs

Q-enhanced LC-based active BPFs mainly use transformer feedback [66], [67] and tapped-inductor feedback [36], [68] architectures. The tapped-tapped-inductor feedback technique provides a high inductance value, low power dissipation and small size compared to the conventional transformer feedback topology. Nevertheless, active BPFs realised with both of these topologies have the disadvantages of relatively high NF and power consumption. These topologies generally use common-source or common-gate series feedback structures, which

-R_N -R_N λ/4 resonator λ/4 resonator

C_C3 C_C2

C_C1

Inductive cross-coupling I/O I/O

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are mostly applied in oscillator circuits. Owing to the series feedback structure, the noise performance of active BPFs is degraded [8].

The Q-enhanced semi-passive inductor with the tapped-inductor feedback technique is illustrated in Figure 2.7.

Figure 2.7. Schematic of the Q-enhanced semi-passive inductor [36] (© [2012] PIER).

In Figure 2.7, the resistor R has a high resistive value, which blocks RF signals and eliminates the requirement for an RF choke. The tapped inductor is connected to the source terminal of the NMOS transistor M1. The approximated expression of the input impedance Zin for this mutual inductance and transconductance of M1, respectively. The real part of input impedance contains resistive losses of L1 and L2, and negative resistances associated with M, gm, L2 and C.

Therefore, the resistive losses of Zin are compensated for by both M and L2. Compared to the transformer feedback topology, where losses are compensated for only by M, the tapped-inductor feedback topology [36] displays a low power implementation. Furthermore, the

V_G V_D

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imaginary part of Zin holds L1 as well as L2 and 2M, which eventually increases the inductance value with this topology.

2.5.3.2 Active capacitance-based BPFs

In low GHz (less than 10 GHz) RF IC design, the main challenge is the low Q-factors of on-chip passive inductors. The IL of active BPFs at these frequencies is mostly governed by the low Q of these inductors. In mm-wave frequency band, passive inductors show desirable Q-factors of 15 or more [25], [69]. The Q-factors of on-chip passive inductors increase with increasing frequencies, while those of on-chip passive capacitors tend to decrease. Therefore, in mm-wave filters, the IL is mainly affected by the Q-factors of capacitors. The NF also depends on the IL value, so the IL and NF can both be reduced by using high-Q capacitors in active filters [30]. Furthermore, with increasing frequencies, the capacitance values of on-chip passive capacitors increase. The low Q-factors and deviation in capacitance values with frequencies are serious drawbacks of these capacitors. Consequently, the overall performance of mm-wave ICs is significantly degraded.

On-chip active capacitors are a better substitute for on-chip passive capacitors. Active capacitors are constructed with transistors and possess high Q-factors and tunable capabilities.

These high-Q capacitors can be used for loss and noise performance improvement of mm-wave active BPFs. Q-enhanced LC-based active BPFs show poor noise and power performance, but the BPFs realised with the active capacitance technique do not have such types of demerits.

BPFs with the active capacitance method for resistive loss compensation are reported in [8], [30].

Figure 2.8(a) presents the active capacitance circuit consisting of three NMOS transistors. The value of Zin of this circuit is defined by the parallel combination of a negative resistance RN and a capacitance CT, as shown in Figure 2.8(b). NMOS transistor M3 of Figure 2.8(a) works as a load resistor and modulates the gate voltage of the driver transistor M2. Transistor M1 of the cross-coupled pair acts as an active switch. Transistors M1 and M3 also control the range of negative resistance. The layout dimension of M2 is a key factor in high-current operation.

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(a)

(b)

Figure 2.8. (a) Active capacitance schematic representation, (b) Equivalent model [8]

(© [2014] IET).

From Figure 2.8(b), the expression of input admittance Yin is represented by (2.11).

1 1

in T

in N

Y j C

Z R 

   (2.11)

V_G V_D

Z_in

i_D

M₂ M₃

M₁

R_N Z_in

C_T

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The Q-enhanced resonator incorporating the active capacitance circuit of Figure 2.8 is demonstrated in Figure 2.9.

Figure 2.9. Q-enhanced resonator with active capacitance circuit [8] (© [2014] IET).

The schematic of Figure 2.9 comprises two inductors LC and LS, and a capacitor CB. The inductor LC blocks RF signals, LS is for the resonator, and CB blocks DC signals. The resistor RS shows the resistive losses of LS.

2.5.3.3 Q-enhanced TL-based active BPFs

Active BPFs are proposed using Q-enhanced TL-based techniques, such as cross-coupled pair [26]-[28], [70] and coupled negative resistance [71], [72]. Different cross-coupled pair architectures are applied to the resonator to compensate for the resistive losses, including NMOS cross-coupled pair [28], [70], [73] and complementary cross-coupled pair [26], [27], [35].

Figure 2.10(a) shows the Q-enhanced TL-based resonator comprising a differential NMOS cross-coupled pair, and Figure 2.10(b) presents its equivalent circuit model.

V_G V_D

M₂ M₃

M₁

L_C

C_B

R_S

L_S

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(a)

(b)

Figure 2.10. (a) Q-enhanced resonator with cross-coupled pair, (b) Equivalent circuit [28]

(© [2008] IEEE).

In Figure 2.10, -GN represents the negative conductance provided by an NMOS cross-coupled pair that compensates for the resistive losses of the passive resonator. The negative conductance is produced only with differential excitation and is represented by (2.12). The parameters Geq and Ceq are the equivalent conductance and equivalent capacitance of the Q-enhanced resonator, respectively. The expressions of Geq and Ceq are given by (2.13) and (2.14), respectively. In these equations, Yc, α and l are the characteristic admittance, attenuation constant and length of the TL, respectively [28].

2

m N

G g

   (2.12) G_eq Y_cl (2.13)

M₂ M₁

TL-based

resonator

A₁ A₂

-G_N L_eq

C_eq

G_eq

A₁ A₂

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A second-order CMOS active BPF with two Q-enhanced TL-based resonators of Figure 2.10 is shown in Figure 2.11.

Figure 2.11. Schematic of TL-based second-order active BPF [28] (© [2008] IEEE).

In the schematic of an active BPF presented in Figure 2.11, the biasing and tuning circuits controlled by VTUNE provide biasing currents for the NMOS cross-coupled pair. The reference impedance of the input and output ports is 50 Ω. The realisation of passive resonators by using synthetic quasi-TEM TLs, also known as complementary conducting strip TLs (CCS TLs), is reported in [26], [27], [35] and [40]. The application of CCS TL was first published in 2004 [74]. Compared to the conventional thin-film microstrip line, CCS TL can provide more parameters for the guiding characteristics synthesis without any change in the process and

M₂

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material constants. In addition, CCS TL can be meandered in the two-dimensional plane with fewer coupling effects [74]. Efficiently meandered CCS TL can provide compact layout, size miniaturisation and a high degree of integration [35]. All these attractive features of CCS TL support its application in MMICs and SOC implementation. A modified form of CCS TL, known as condensed complementary conducting strip TL (C-CCS TL) is proposed in [70] for passive resonator realisation. C-CCS TL has great capacity for further area reduction. Both the CCS TL and C-CCS TL facilitate size minimisation and Q-factor improvement simultaneously and can, therefore, be considered in the research of TL-based compact mm-wave BPFs.