# A Wide Tuning-Range CMOS VCO with a Tunable Active Inductor

Authors: Hsuan-Ling Kao; Ping-Che Lee; Hsien-Chin Chiu
Journal: Mathematical Problems in Engineering
 (2015)

---

## Abstract

This study describes a wide tuning-range VCO using tunable active inductor (TAI) topology and cross-coupled pair configuration for radio frequency operation. The TAI used two feedback loops to form a cascode circuit to obtain more degrees of freedom for inductance value. The TAI-VCO was fabricated using a 0.18μm CMOS technology. The coarse frequency tuning is achieved by TAIs while the fine tuning is controlled by varactors. The fabricated circuit provides an output frequency range from 0.6 to 7.2 GHz (169%). The measured phase noise is from −110.38 to −86.01 dBc/Hz at a 1 MHz offset and output power is from −11.11 to −3.89 dBm within the entire frequency range under a 1.8 V power supply.


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## Body

## 1. Introduction

The rapidly developing wireless and communication systems make the multiband RF terminals from several hundred megahertz to gigahertz frequency coexist. Integrated multiband wireless blocks in one-chip IC are demanded for high-speed, high-functionality, small-size, and low-cost communication systems. One of the key building blocks is fully integrated voltage controlled oscillators (VCOs). The challenges of the VCO circuit are die size, cost, and power dissipation. The general VCO circuits used spiral inductors and varactors to realize the circuit. However, the on-chip spiral inductors have a small inductance value per unit area and lowQ-factor because of losses of Si-substrate. It also occupied a large chip size. The varactors limited the tuning range within 30% due to the maximum to the minimum capacitance ratio of the varactor and the parasitic effect [1–3]. Therefore, various techniques have been proposed to enhance the tuning range of VCOs, such as switched capacitor arrays [4–8], switched inductors [9–11], and tunable active inductors (TAIs) [12–16]. TAI is one of the good candidates due to its small size, high Q, widely tunable inductance, and large inductance compared to those of the spiral inductor [17, 18]. The tuning range of 120% (0.5~2 GHz) is achieved in a single-end VCO circuit with a TAI tuned by tunable feedback resistance [14]. A differential TAI is proposed to achieve a 0.5~3 GHz (143%) tuning range and −118 dBc/Hz at a 1 MHz offset at 690 MHz [15]. However, the operation frequencies are lower than 3 GHz because the traditional active inductor is difficult to operate at higher frequency due to a large parasitic load capacitance. The cascode active inductor (AI) is proposed to enhance the resonance frequency [17]. In this study, by utilizing a tunable cascade active inductor, the VCO circuit exhibits a very wide frequency tuning range and also enhances output power and phase noise. The TAI-VCO provides an output frequency which ranges from 0.6 to 7.2 GHz (169%). The paper is organized as follows. Section 2 outlines tunable active inductor design. Section 3 presents the TAI-VCO circuit design. Section 4 presents the TAI-VCO measurement results. Finally, concluding remarks are offered.


## 2. Tunable Active Inductor Design

Figure1 shows that the proposed AI circuit consists of four transistors (M
1

~

M
4) and three current sources (I
1

~

I
3). Two feedback loops are formed in this circuit. Transistors M
1 and M
2 make up the first feedback loop and M
3 and M
4 form the second loop. The cascode technique is used to reduce output conductance and enhance the gain for high frequency. Transistor M
3 is stacked on top of transistor M
1. For increasing the cascode effect, the additional gain stage was implemented by M
4. The addition of transistor M
4 does not degrade the high frequency response of the inductor, because the signal path is still through M
1, M
2, and M
3. To analyze the response of the TAI, the simplified small signal model and equivalent circuit model are shown in Figure 2.Figure 1
Schematic of cascode active inductor.Figure 2
(a) Small-signal equivalent circuit and (b) equivalent circuit model of the AI.
(a)
(b)The input admittance from the input port is given by the following equation:(1)
Y
in
=
s
C
gs
1
+
g
m
1
g
m
2
s
C
gs
2
1
+
s
C
gs
3
/
g
m
3
+
s
2
C
gs
3
/
g
m
3
C
gs
4
/
g
m
4
+
g
m
1
1
+
s
C
gs
3
/
g
m
3
+
s
2
C
gs
3
/
g
m
3
C
gs
4
/
g
m
4
,where g
m
1

~

g
m
4 are the transconductance of the transistors M
1
–
M
4. C
gs and C
gd are gate-source capacitance and gate-drain capacitance of the corresponding transistors, respectively. The C
gs is much greater than C
gd. The C
gd was ignored in the small signal model. Assume that the operating frequency (ω) of the active inductor is much lower than the cutoff frequency (ω
t
=
g
m
/
C
gs) of the transistors. Compare (1) with the equivalent circuit in Figure 2(b) with the following values:(2)
C
eq
≈
C
gs
1
(3)
G
p
=
1
R
p
≈
g
m
1
1
-
ω
2
C
gs
4
C
gs
3
/
g
m
3
g
m
4
=
g
m
1
1
-
ω
2
/
ω
t
3
ω
t
4
(4)
L
eq
≈
C
gs
2
g
m
1
g
m
2
(
1
-
ω
2
C
gs
3
C
gs
4
g
m
3
g
m
4
)
=
1
g
m
1
ω
t
2
(
1
-
ω
2
ω
t
3
ω
t
4
)
(5)
R
eq
≈
-
ω
2
C
gs
2
C
gs
3
g
m
1
g
m
2
g
m
3
=
-
ω
2
C
gs
2
g
m
1
g
m
2
ω
t
3
=
-
ω
2
g
m
1
ω
t
2
ω
t
3
,where ω
t
1

~

ω
t
4 are the transconductance of the transistors M
1
–
M
4. R
eq is very small because its value is a second-order effect. We neglect the R
eq in the following derivation of resonant frequency (ω
RES) of the active inductor which is given by (6)
ω
RES
=
g
m
1
g
m
2
C
gs
1
C
gs
2
(
1
-
ω
2
C
gs
3
C
gs
4
/
g
m
3
g
m
4
)
=
ω
t
1
ω
t
2
1
-
ω
2
/
ω
t
3
ω
t
4
.To evaluate the broadband characteristics of the active inductors, the quality factor (Q-factor) is defined as the ratio of the imaginary part to the real part of the input impedance, which can be approximated by(7)
Q
≈
ω
2
C
gs
1
g
m
1
C
gs
2
g
m
2
-
ω
2
C
gs
2
g
m
2
C
gs
3
g
m
3
h
l
+
ω
2
C
gs
4
g
m
4
C
gs
3
g
m
3
-
1
ω
C
gs
2
g
m
2
-
ω
C
gs
3
g
m
3
-
1
=
ω
2
/
ω
t
2
ω
t
1
-
ω
2
/
ω
t
2
ω
t
3
+
ω
2
/
ω
t
3
ω
t
4
-
1
ω
/
ω
t
2
-
ω
/
ω
t
3
.From (4) and (6), it is observed that L
eq is inversely dependent on g
m
1
×
ω
t
2 and ω
RES is dependent on (
ω
t
1
ω
t
2
)
1
/
2. The cutoff frequency of cascode transistors ω
t
3 and ω
t
4 decreased L
eq and increased G
p and ω
RES. The small inductance and higher resonance frequency of AI provide high operation frequencies.To achieve the tunable active inductor,M
5 is used as a current source (I
2) controlled by gate voltage (V
ctrl) as shown in Figure 3. The device gate width of M
1

~

M
5 is 6 × 64, 3 × 40, 8 × 64, 6 × 64, and 1.5 × 25 μm, respectively. The R
1 is a current source of 156 Ω. Figure 4 shows that the g
m
1 and ω
t
2 are dependent on V
ctrl. The larger the V
ctrl is, the larger the g
m
1 and ω
t
2 are. According to (4) and (6), the inductance and resonant frequency of TAI can be tuned by V
ctrl. The inductance and Q-factor of TAI can be carried by controlling V
ctrl as the prediction of (4) and (6)-(7).Figure 3
Tunable cascode active inductor byV
ctrl.Figure 4
Simulatedω
t
2 and g
m
1 of the TAI with V
ctrl.


## 3. VCO Circuit Design

Figure5 shows the proposed VCO where the LC-tank is composed of a TAI and a varactor (C
v) for frequency and the negative conductance (-
G
m) is employed to compensate for the loss from the LC-tank. The symmetric components are identical. The cross-coupled pair VCO circuit is composed of M
6, M
7, C
v
1, C
v
2, C
1, C
2, TAI1, and TAI2. The device gate widths of M
6 and M
7 are 50 μm with six gate fingers. C
1 and C
2 are DC block capacitors. Figure 6 shows mechanisms of oscillator frequency tuning using TAIs and varactors [12]. The TAIs can be tuned over a wide range to provide coarse frequency tuning. The varactors provide a fine tuning range and LC-tank topology. Coarse tuning was achieved by TAIs and fine tuning was achieved by changing varactors. For coarse frequency tuning, TAI inductance is controlled by the controlled voltage (V
ctrl). For fine frequency tuning, the varactor capacitance is controlled by the varactor voltage (V
c). The cross-coupled pair differential VCOs are convenient to connect directly to a differential input, such as a balanced mixer in an integrated circuit system.Figure 5
Schematic of the proposed TAI-VCO.Figure 6
Mechanisms of coarse and fine tuning of the proposed TAI-VCO.The noise current injected at output nodes is composed of two parts,i
n
,
TAI
2
¯ and i
n
,
CC
2
¯, representing the contribution of TAI and cross-coupled pair (CC) transistors, respectively. The noise current typically is the channel-induced noise and gate-induced noise of a transistor. The total noise current of output nodes can be written as (8)
i
n
,
total
2
¯
Δ
f
=
2
i
n
,
TAI
2
¯
Δ
f
+
i
n
,
CC
2
¯
Δ
f
.The total single-sideband phase noise spectral density at an offset frequency of Δ
ω is given by(9)
L
{
Δ
ω
}
=
10
log
⁡
∑
n
=
0
∞
C
n
i
n
,
total
2
¯
/
Δ
f
4
q
max
⁡
2
Δ
ω
2
,where C
n represents the coefficients in the Fourier series of the impulse sensitivity function and q
max
⁡ is the maximum charge swing across the current noise source. The TAI and CC are composed of five and two transistors, respectively. The phase noise of TAI-VCO is larger than LC-VCO due to the number of transistors. However, the output power is also an important parameter of VCO. The coarse frequency tuning of the cascode TAI was controlled by V
ctrl. As V
ctrl increases, M
5 was driven from triode region to saturation region, resulting in larger bias current and larger drain voltage for the cross-coupled pair. Therefore, the larger drain voltage of the cross-coupled pair provided larger output swing at higher frequency while decreasing equivalent inductance and increasing oscillation frequency. A uniform output power can be achieved over the whole frequency range in the proposed TAI-VCO topology.


## 4. Measurement Results

The cross-coupled pair VCO was simulated, using Advance Design System (ADS) software. The layout of the circuit, especially the symmetry of the cross-coupled design, plays an important role in circuit design. The top-layer metal and bottom-layer metal crossing and the difference between path lengths are crucial to ensure balanced signals and a compact size. Figure7 shows the layout of the fabricated VCO. Its size is 0.835 × 0.615 mm2, including the probe pads. The TAI-VCO was tested on a wafer—the spectral density of the circuit being measured with a spectrum analyzer. The circuit is biased at V
DD
=
1.8 V, V
g
=
0.7 V, I
total
=
23

~

27 mA, V
ctrl
=
1.4

~

2.7 V, and V
c
=
0.5

~

2.0 V. The power consumption of the VCO is 41

~

49 mW, from a 1.8 V power supply.Figure 7
Photograph of the fabricated VCO.Figure8 shows the tuning range of the TAI-VCO circuit. The proposed cross-coupled pair VCO was tuned, from 0.6 GHz to 7.2 GHz, which is a tuning range of 6.5 GHz (near 169% tuning range). Figure 9 shows the phase noise and output power of the TAI-VCO circuit. The VCO has phase noise, of −110.38 and −99.04 dBc/Hz, at a 1 MHz offset from 0.63 and 7.2 GHz carrier, respectively. Within the VCO tuning range, the variations in output power are −7.64 ± 3.5 dBm. The output spectrum and phase noise of the proposed TAI-VCO at 630 MHz, 2.7 GHz, and 7.2 GHz are shown in Figure 10. The lowest phase noise is −110.38 dBc/Hz, at 1 MHz offset from the 0.629 GHz carrier frequency. The maximum output power is −3.89 dBm, including a 4.7 dB loss due to implementation, and operates at 2.7 GHz under a 1.8 V power supply. Table 1 summarizes the measured performance of the VCO and includes other reported performances, for the purpose of comparison [7–9, 13–16].Table 1
Comparison of VCO circuit performance: published and this work.
Unit
This work
[7]
[8]
[9]
[13]
[14]
[15]
[16]*
Tuning range
GHz
0.6~7.2
3.2~5.3
3.3~5.1
1.1~1.9
1.1~2.7
0.5~2
0.5~3
1.3~2.2
%
169
47.7
41.1
51
81
120
143
47.5
KVCO
MHz/V
5,000
167~555
50~85
667
3,850
500
2,500
458
P
out
dBm
−3.89~−11.1
−4.8
−7
—
−14.28
−21~−29
−14~−22
−9~−16
PN at 1 MHz offset
dBc/Hz
−86~−110
−115.6
−123.14
−126
−83~−92
−78~−90
−101~−118
−82~−86
Area
mm2
0.51
0.828
0.24
0.5
0.4
0.09
0.45
—
Architecture
TAI
Switched-cap.
Switched-cap.
Switched-ind.
TAI
TAI
TAI
TAI
*Simulated results.Figure 8
Measured oscillation frequency againstV
ctrl and V
c.Figure 9
Measured phase noise and output power against control voltageV
ctrl.Figure 10
Output spectrum and phase noise of the proposed VCO at (a) 630 MHz, (b) 2.7 GHz, and (c) 7.2 GHz.
(a)
(b)
(c)


## 5. Conclusion

The fully integrated VCO with tunable active inductor on 0.18μm CMOS technology demonstrated good circuit performance, in terms of a wide tuning range, high output power, and low phase noise. This TAI-VCO displayed a wide frequency range from 0.6 to 7.2 GHz, resulting in a tuning range of 169% at radio frequency. The lowest phase noise was −110.38 dBc/Hz, at a 1 MHz offset from a 630 MHz carrier and a highest output power of −3.89 dBm at 2.7 GHz under a 1.8 V power supply.



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*Source: 382483-2015-03-04.xml*