analysis of emitter degenerated lc oscillators using bipolar technologies
ANALYSIS OF EMITTER DEGENERATED LC OSCILLATORS USING BIPOLAR TECHNOLOGIES J. H. C. Zhan, K. Maurice, J. S. Duster, K. T. Kornegay Cornell Broadband Communications Research Laboratory Cornell University Ithaca, New York 14853, USA
ABSTRACT The effects of emitter degeneration on the oscillation frequency, output noise and tuning range of an emitter degenerated LC oscillator designed using bipolar transistors (BJT) is analyzed. Simulation results show increased oscillation frequency, tuning range and carrier-to-noise ratio (CNR). Design guidelines for emitter degenerated LC oscillators are also given.
1. INTRODUCTION Among the many different VCO topologies available, the LC oscillator in Figure 1 is one of the most commonly used due to its simplicity. According to Leeson’s formula, the phase noise in the 1/f2 region at an offset frequency ∆ω from an oscillation frequency of ωOSC, is given in equation (1) [1],
PNw( ∆ω ) = kTR
F Vo
2
(
ω OSC 2 ) Q∆ω
(1)
L
2. NEGATIVE IMPEDANCE TRANSFORMATION One function of a cross-coupled transistor pair is known, to first order, to perform negative impedance transformation [2,3], as shown in Figure 2 (a). If two capacitors (CE) are placed at the emitters of the cross-coupled pair, ideally the input impedance looking into the cross-coupled pair will be -CE/2, thereby increasing
the
oscillation
frequency
from
1 / 2π LC
to 1 / 2π L(C − CE ) . Another benefit is the increased tuning range. Let the tuning range of the varactor be C±∆C. Then, the tuning range before and after emitter degeneration, in terms of percentage, will be given by ±100∆C/C and ±100∆C/(C- CE), respectively. ZIN
where k, T, R, Vo, Q and F are the Boltzmann’s constant, the absolute temperature, the equivalent tank parallel resistance, the peak oscillation amplitude, the tank quality factor, and the noise factor, respectively. For the oscillator in Figure 1, the process dependent inductor dominates the Q of the tank, and the output voltage, Vo, decreases with frequency because of transistor gain decrease. Therefore, for a given process, without any circuit modifications, the CNR and oscillation frequency cannot increase simultaneously. R
in Section 3. Simulation results are given in Section 4 followed by conclusions in Section 5.
ZIN (a) ideal transformation
ZE
ZE Z =R //C E E E in later discussion
-ZE
ZIN
ZIN -1/gm
ZE
-ZE
ZE
-1/gm
-sCπrb/gm (b) more accurate transformation -Z
E
-sCπrb/gm -ZE
C
Figure 2 Negative impedance transformation (ZE = RE // CE in later discussion).
Figure 1 A typical LC oscillator using a cross-coupled transistor pair. In the sections that follow, we will show how to use emitter degeneration to simultaneously increase the oscillation frequency, the tuning range and the CNR of an LC oscillator. Using the negative impedance transformation described in Section 2, we derive useful design equations which are presented
The above reasoning, although intuitive, does not provide useful design insights. In the following derivation, a small signal model and a real gm are used. The effects of large signal distortion and phase shift caused by gm [4] are verified using simulation. Our intention is not to derive exact solutions but instead, to provide design equations or boundary conditions that are useful in early design stage. A more accurate negative impedance transformation is shown in Figure 2 (b). Denote the current gain, base resistance, conductance and base-emitter capacitance by β, rb, gm and Cπ, respectively, then the transformed negative impedance can be expressed as:
Z IN , RLC −in −collector −excluded =
β +1 β 1 β sCπ rb ) + ZE + β −1 β −1 gm β −1 gm C r 1 1 + sL E ) ≈ − 2( Z E + + s π b ) ≡ −2( Z E + gm gm gm
− 2(
R= 100Ω
(2)
L= 0.2nH
C= 600fF
R= L= 100Ω 0.2nH Vo-
Vo+
0.32um x 7um
In addition to ZΕ (=RE//CE), the transistors also introduce additional impedances 1/gm and sCπrb/gm, where the latter is denoted by sLE because it has the functional form of an inductor. RE
3. DESIGN EQUATIONS Using the negative impedance transformation method described in previous section, we analyze the constraints required to sustain oscillation and determine the oscillation frequency. Noise performance of the degenerated oscillator is also presented. Our analysis is based on the linear time invariant (LTI) model. Liner time varying (LTV) model [5, 6] analysis can also be performed if necessary. All assumptions required for analysis will be addressed in the section that follows.
VDD=3.3V C= 600fF
CE
RE
CE
8.2mA
(a) R
L
R
C
L
C
3.1 Condition
to sustain oscillation and oscillation frequency Denote the real part and imaginary part of the transformed negative impedance by REE and XEE, then the overall tank impedance as viewed from the collectors is given by Z IN , RLC − in − collector − included 2
=
(3)
Z IN , RLC −in −collector −excluded //( RLC − in − collector )
( R − ω LCR ) REE
ωLR (− X EE + jREE ) − ωLX EE + j{ωLREE + X EE ( R − ω 2 LCR ) − ωLR}
To excite oscillation, the real part of ZIN must be negative. Therefore, the oscillation frequency is where the imaginary part of ZIN becomes zero. These two conditions lead to: 2 X EE R > R EE + R EE 2 2 2 ( R EE + X EE )(1 − ω OSC LC ) X EE = ω OSC L
(b) Figure 3 Example emitter degenerated VCO circuit topologies.
3.1.1 Case I: Non-Degeneration
2 2
CE
CE
(4)
The condition to sustain oscillation is determined by g m > 1 /{R − g m (ωL E ) 2 } > 1 / R , which indicates that the power required to sustain oscillation is higher than the generally known lower bound of 1/R. Moreover, this power increases with oscillation frequency. This can be observed from Figure 2 (b) directly where sLE dominates the negative impedance at high frequencies, thus the required negative resistance 1/gm will lose its expected functionality eventually. In this case the oscillation frequency is given by 2 LCω OSC
2
(5)
2
For the VCO in Figure 1, REE=1/gm and XEE=ωLE. For the emitter degenerated VCO, we are interested in placing two capacitor CE at the emitters of the cross-coupled transistor pair, thus REE =1/gm and XEE=(ωLE-1/ωCE), as illustrated in Figure 3. A comparison between the two VCO in Figure 3 reveals that the VCO in Figure 3 (a) consumes more voltage headroom because of the voltage drop across RE and also has extra noise sources RE, while the VCO in Figure 3 (b) does not have an RE explicitly, because RE is equal to the output resistance of the tail current bias circuit, and the output capacitance of the tail current bias circuit introduces additional degenerating capacitance. In either case, the design of RE is based on RE >> 1/sCΕ to satisfy the assumption XEE = (ωLE-1/ωCE).
= (1 −
R EE LC LE
2
2
−
R LC L 2 LCR EE L ) + (1 − EE 2 − ) +4 2 LE LE LE LE
2
0 , to increase its oscillation frequency, a smaller gm is required. This contradicts to the first constraint, which requires a high enough gm to sustain oscillation, and in some cases no gm exists to satisfy both conditions.
3.1.2 Case II: Emitter Degeneration For the emitter degenerated VCO, the requirement to sustain oscillation is g m > 1 /{R − g m (ωL E − 1 / ωC E ) 2 } . Note that the expression in the right-hand side no longer increases monotonically with frequency, and its value can be made smaller than that without degeneration. The oscillation amplitude is also increased because now, gm acts as negative resistance more effectively. As for the oscillation frequency, the exact expression is too complicated to extract useful design information. However, since 2 2 2 X EE ω OSC L = ( R EE + X EE )(1 − ω OSC LC ) and if XEE is negative, it is possible for ωOSC to be above 1 / 2π LC , if all previous assumptions are satisfied.
degeneration are –1/gm-jωLE and –1/gm-j(ωLE-1/ωCE), we have only to focus on the effects of XEE on the noise transfer function. 2
Vo [ R ( R − R EE ) − X EE ] + jX EE R = H ( jω ) = − EE 2 VN ( R − R EE ) 2 + X EE ⇒
(6)
R( R − 2 REE ) 2 ∂ H ( jω ) = 2 2 [( R − REE ) 2 + X EE ]2 ∂X EE
If R>2REE or gm>2/R, which we refer to as a rule of thumb, then the noise transferred to the output can be reduced by decreasing |XEE|. Without emitter degeneration, it is impossible to decrease XEE and increase oscillation frequency simultaneously. Thus, by choosing the appropriate value of CE, oscillation frequency, tuning range and CNR can be enhanced simultaneously.
4. SIMULATION RESULTS The analyses above are first verified via circuit simulations containing ideal resistors, capacitors, inductors, current sources, and BJTs from the IBM SiGe 6HP process technology. The parameters used for simulation are shown in Figure 3 (a). The L
Io +Vo
-Vo
+Vi
-Vi
H2(jω) VN1 CE
RE
+ -
VN
H1(jω)
IDC
Figure 4 The effects of emitter degeneration resistance on output noise.
3.2 Noise Analysis We now focus our discussion on the noise performance of the circuit in Figure 3 (a). Compared to the non-degenerated version, both the oscillation frequency and amplitude increase, therefore the phase noise does not necessarily degrade. The additional thermal noise introduced by RE can be analyzed as follows. Consider Figure 4 where the noise generated by RE is filtered by a low-pass filter H1(jω) whose 3dB corner frequency is 1/CERE, then by H2(jω). Since in the vicinity of oscillation frequency, the parallel RLC tank impedance is dominated by R, |H2(jω)| can be approximated by 1 / 1 + (ωCπ rb / Rg m ) 2 , which is also a lowpass filter. Hence, the effects of the noise introduced by RE is alleviated. Another effect of this topology is that the noise shaping function is modified. Let’s consider the noise introduced by R. Again we assume that at the frequency range of interest, only R is important. Since the negative impedance without and with
and C values used yield an oscillation frequency of 1 / 2π LC = 14.53GHz, and the chosen R produces a Q factor of approximately 5 for the inductor. The simulated oscillation frequency in Figure 5 is determined where the imaginary part of the impedance is zero while the real part of the impedance remains negative. The oscillation frequency without emitter degeneration is only 9.79 GHz, which is outside of the scale of the plot in Figure 5. It is possible to have an oscillation frequency greater than 14.53GHz as shown in Figure 5. This is true for certain values of CE because of the requirement that ωLE1/ωCE be negative. Also note that without CE, the increase in RE will eventually prevent oscillation, as predicted for the nondegenerated case in section 3. The output phase noise at a 2MHz offset is given in Figure 6. Note that if CE is too small, it does not filter out the noise generated by RE, and it also increases |XEE|, which leads to a degradation in CNR. The effect on tuning range is also examined. Without emitter degeneration, when the capacitance at the collector sweeps from 600fF to 800fF, the oscillation frequency changes from 9.78 to 9.06GHz. Using the degeneration impedance of RE=300Ω and CE=250fF, the oscillation frequency changes from 14.60 to 12.90 GHz. Either in terms of the tuning range or in terms of percentage of tuning range, the degenerated oscillator exhibits superior performance over its non-degenerated counterpart. Using the simple design equations described in Section 3, several VCOs using emitter degeneration are designed and simulated. The first design contains two VCOs, one emitter degenerated and the other without degeneration, for comparison. The layouts of the two VCOs differ only in the degeneration impedances, and including output buffers they each consumes 430 um x 225 um chip area. The power and ground for the two VCOs are separated to avoid signal coupling. The power consumption for the VCO core and buffers are 27mW and 50mW, respectively. For the degenerated VCO, the simulated tuning range is 26.2 to 27.09 GHz, the phase noise at a 2MHz offset is 96.4 dBC/Hz, compared to 15.68 to 16.08 GHz and -89.6 dBC/Hz for the nondegenerated case.
The second example can be used in wired optical line applications such as SONET192. Simulation results reveal that the oscillation frequency ranges from 10.2 to 10.9 GHz, the phase noise is –101dB at a 1MHz offset, and the power consumption is 31mW including the output buffers. Its nondegenerated counterpart does not oscillate because the negative impedance is dominated by sLE rather than gm.
RE=50
RE=100 RE=150 14.0
RE=200 RE=300
5. CONCLUSIONS
RE=400
13.5
RE=500 RE=600 13.0
12.5
From an intuitive viewpoint, this paper analyzes the use of emitter degeneration to increase the oscillation frequency, tuning range and CNR of an LC oscillator. Design equations are provided that give reasonable prediction of circuit performance as verified by simulation and later, experimentally.
12.0
11.5 0
6. ACKNOWLEDGEMENT The authors would like to express their gratitude to IBM Microelectronics for support of this research.
RE=75
14.5
Oscillation Frequency (GHz)
The third design example is targeted for wireless applications around 2.1GHz. The emitter degenerated VCO oscillates from 2.14 to 2.37 GHz, exhibits a phase noise of –118dB at a 1MHz offset, and consumes 15mW. Without emitter degeneration, it oscillates from 1.65 to 1.77GHz, and its phase noise is –116.7dB at 1MHz while consuming the same power. It is also interesting to note that the amplitude of the oscillation signal is 840 and 750 mV peak to peak for the degenerated and non-degenerated VCOs. The reason why the former oscillates at a higher frequency at larger oscillation amplitudes is given in Section 3.
No degeneration, 9.79GHz RE=25
15.0
200
400
600
800
1000
1200
Degeneration Capacitance (fF)
Figure 5 Plot of oscillation frequency as a function of degeneration capacitance.
7. REFERENCES -90.00 0
200
400
600
800
1000
RE=0 RE=25 RE=50 RE=75
-94.00
RE=100 RE=150 RE=200 RE=300 RE=400
-98.00
RE=500
Phase Noise (dB)
[1] D. B. Leeson, “A Simple Model of Feedback Oscillator Noise Spectrum,” in Proc. IEEE, vol. 54, Feb. 1966, pp.329330. [2] T. H. Lee and J. F. Bulzacchelli, “A 155-MHz clock recovery delay-and phase-locked loop,” IEEE J. Solid-State Circuits, vol. 27, pp. 1736-1746, Dec. 1992. [3] W.Z. Chen and J. T. Wu, “A 2-V 2-GHz BJT Variable Frequency Oscillator,” IEEE J. Solid-State Circuits, vol. 33, pp. 1406-1410, Sep. 1998. [4] Johan D. van der Tang, Dieter Kasperkovitz and Arthur van Roermund, “A 9.8-11.5GHz Quadrature Ring Oscillator for Optical Receivers,” IEEE J. Solid-State Circuits, vol. 37, pp. 438-442, Mar. 2002. [5] A. Hajimiri and T. H. Lee, “A General Theory of Phase Noise in Electrical Oscillators,” IEEE J. Solid-State Circuits, vol. 33, pp. 179-194, Feb. 1998. [6] A. Hajimiri and T. H. Lee, “Oscillator Phase Noise: A Tutorial,” IEEE J. Solid-State Circuits, vol. 33, pp. 326-336, Mar. 2000.
RE=600
-102.00
-106.00
-110.00 Degenerated Cap (fF)
Figure 6 Simulated phase noise.
1200
ABSTRACT The effects of emitter degeneration on the oscillation frequency, output noise and tuning range of an emitter degenerated LC oscillator designed using bipolar transistors (BJT) is analyzed. Simulation results show increased oscillation frequency, tuning range and carrier-to-noise ratio (CNR). Design guidelines for emitter degenerated LC oscillators are also given.
1. INTRODUCTION Among the many different VCO topologies available, the LC oscillator in Figure 1 is one of the most commonly used due to its simplicity. According to Leeson’s formula, the phase noise in the 1/f2 region at an offset frequency ∆ω from an oscillation frequency of ωOSC, is given in equation (1) [1],
PNw( ∆ω ) = kTR
F Vo
2
(
ω OSC 2 ) Q∆ω
(1)
L
2. NEGATIVE IMPEDANCE TRANSFORMATION One function of a cross-coupled transistor pair is known, to first order, to perform negative impedance transformation [2,3], as shown in Figure 2 (a). If two capacitors (CE) are placed at the emitters of the cross-coupled pair, ideally the input impedance looking into the cross-coupled pair will be -CE/2, thereby increasing
the
oscillation
frequency
from
1 / 2π LC
to 1 / 2π L(C − CE ) . Another benefit is the increased tuning range. Let the tuning range of the varactor be C±∆C. Then, the tuning range before and after emitter degeneration, in terms of percentage, will be given by ±100∆C/C and ±100∆C/(C- CE), respectively. ZIN
where k, T, R, Vo, Q and F are the Boltzmann’s constant, the absolute temperature, the equivalent tank parallel resistance, the peak oscillation amplitude, the tank quality factor, and the noise factor, respectively. For the oscillator in Figure 1, the process dependent inductor dominates the Q of the tank, and the output voltage, Vo, decreases with frequency because of transistor gain decrease. Therefore, for a given process, without any circuit modifications, the CNR and oscillation frequency cannot increase simultaneously. R
in Section 3. Simulation results are given in Section 4 followed by conclusions in Section 5.
ZIN (a) ideal transformation
ZE
ZE Z =R //C E E E in later discussion
-ZE
ZIN
ZIN -1/gm
ZE
-ZE
ZE
-1/gm
-sCπrb/gm (b) more accurate transformation -Z
E
-sCπrb/gm -ZE
C
Figure 2 Negative impedance transformation (ZE = RE // CE in later discussion).
Figure 1 A typical LC oscillator using a cross-coupled transistor pair. In the sections that follow, we will show how to use emitter degeneration to simultaneously increase the oscillation frequency, the tuning range and the CNR of an LC oscillator. Using the negative impedance transformation described in Section 2, we derive useful design equations which are presented
The above reasoning, although intuitive, does not provide useful design insights. In the following derivation, a small signal model and a real gm are used. The effects of large signal distortion and phase shift caused by gm [4] are verified using simulation. Our intention is not to derive exact solutions but instead, to provide design equations or boundary conditions that are useful in early design stage. A more accurate negative impedance transformation is shown in Figure 2 (b). Denote the current gain, base resistance, conductance and base-emitter capacitance by β, rb, gm and Cπ, respectively, then the transformed negative impedance can be expressed as:
Z IN , RLC −in −collector −excluded =
β +1 β 1 β sCπ rb ) + ZE + β −1 β −1 gm β −1 gm C r 1 1 + sL E ) ≈ − 2( Z E + + s π b ) ≡ −2( Z E + gm gm gm
− 2(
R= 100Ω
(2)
L= 0.2nH
C= 600fF
R= L= 100Ω 0.2nH Vo-
Vo+
0.32um x 7um
In addition to ZΕ (=RE//CE), the transistors also introduce additional impedances 1/gm and sCπrb/gm, where the latter is denoted by sLE because it has the functional form of an inductor. RE
3. DESIGN EQUATIONS Using the negative impedance transformation method described in previous section, we analyze the constraints required to sustain oscillation and determine the oscillation frequency. Noise performance of the degenerated oscillator is also presented. Our analysis is based on the linear time invariant (LTI) model. Liner time varying (LTV) model [5, 6] analysis can also be performed if necessary. All assumptions required for analysis will be addressed in the section that follows.
VDD=3.3V C= 600fF
CE
RE
CE
8.2mA
(a) R
L
R
C
L
C
3.1 Condition
to sustain oscillation and oscillation frequency Denote the real part and imaginary part of the transformed negative impedance by REE and XEE, then the overall tank impedance as viewed from the collectors is given by Z IN , RLC − in − collector − included 2
=
(3)
Z IN , RLC −in −collector −excluded //( RLC − in − collector )
( R − ω LCR ) REE
ωLR (− X EE + jREE ) − ωLX EE + j{ωLREE + X EE ( R − ω 2 LCR ) − ωLR}
To excite oscillation, the real part of ZIN must be negative. Therefore, the oscillation frequency is where the imaginary part of ZIN becomes zero. These two conditions lead to: 2 X EE R > R EE + R EE 2 2 2 ( R EE + X EE )(1 − ω OSC LC ) X EE = ω OSC L
(b) Figure 3 Example emitter degenerated VCO circuit topologies.
3.1.1 Case I: Non-Degeneration
2 2
CE
CE
(4)
The condition to sustain oscillation is determined by g m > 1 /{R − g m (ωL E ) 2 } > 1 / R , which indicates that the power required to sustain oscillation is higher than the generally known lower bound of 1/R. Moreover, this power increases with oscillation frequency. This can be observed from Figure 2 (b) directly where sLE dominates the negative impedance at high frequencies, thus the required negative resistance 1/gm will lose its expected functionality eventually. In this case the oscillation frequency is given by 2 LCω OSC
2
(5)
2
For the VCO in Figure 1, REE=1/gm and XEE=ωLE. For the emitter degenerated VCO, we are interested in placing two capacitor CE at the emitters of the cross-coupled transistor pair, thus REE =1/gm and XEE=(ωLE-1/ωCE), as illustrated in Figure 3. A comparison between the two VCO in Figure 3 reveals that the VCO in Figure 3 (a) consumes more voltage headroom because of the voltage drop across RE and also has extra noise sources RE, while the VCO in Figure 3 (b) does not have an RE explicitly, because RE is equal to the output resistance of the tail current bias circuit, and the output capacitance of the tail current bias circuit introduces additional degenerating capacitance. In either case, the design of RE is based on RE >> 1/sCΕ to satisfy the assumption XEE = (ωLE-1/ωCE).
= (1 −
R EE LC LE
2
2
−
R LC L 2 LCR EE L ) + (1 − EE 2 − ) +4 2 LE LE LE LE
2
0 , to increase its oscillation frequency, a smaller gm is required. This contradicts to the first constraint, which requires a high enough gm to sustain oscillation, and in some cases no gm exists to satisfy both conditions.
3.1.2 Case II: Emitter Degeneration For the emitter degenerated VCO, the requirement to sustain oscillation is g m > 1 /{R − g m (ωL E − 1 / ωC E ) 2 } . Note that the expression in the right-hand side no longer increases monotonically with frequency, and its value can be made smaller than that without degeneration. The oscillation amplitude is also increased because now, gm acts as negative resistance more effectively. As for the oscillation frequency, the exact expression is too complicated to extract useful design information. However, since 2 2 2 X EE ω OSC L = ( R EE + X EE )(1 − ω OSC LC ) and if XEE is negative, it is possible for ωOSC to be above 1 / 2π LC , if all previous assumptions are satisfied.
degeneration are –1/gm-jωLE and –1/gm-j(ωLE-1/ωCE), we have only to focus on the effects of XEE on the noise transfer function. 2
Vo [ R ( R − R EE ) − X EE ] + jX EE R = H ( jω ) = − EE 2 VN ( R − R EE ) 2 + X EE ⇒
(6)
R( R − 2 REE ) 2 ∂ H ( jω ) = 2 2 [( R − REE ) 2 + X EE ]2 ∂X EE
If R>2REE or gm>2/R, which we refer to as a rule of thumb, then the noise transferred to the output can be reduced by decreasing |XEE|. Without emitter degeneration, it is impossible to decrease XEE and increase oscillation frequency simultaneously. Thus, by choosing the appropriate value of CE, oscillation frequency, tuning range and CNR can be enhanced simultaneously.
4. SIMULATION RESULTS The analyses above are first verified via circuit simulations containing ideal resistors, capacitors, inductors, current sources, and BJTs from the IBM SiGe 6HP process technology. The parameters used for simulation are shown in Figure 3 (a). The L
Io +Vo
-Vo
+Vi
-Vi
H2(jω) VN1 CE
RE
+ -
VN
H1(jω)
IDC
Figure 4 The effects of emitter degeneration resistance on output noise.
3.2 Noise Analysis We now focus our discussion on the noise performance of the circuit in Figure 3 (a). Compared to the non-degenerated version, both the oscillation frequency and amplitude increase, therefore the phase noise does not necessarily degrade. The additional thermal noise introduced by RE can be analyzed as follows. Consider Figure 4 where the noise generated by RE is filtered by a low-pass filter H1(jω) whose 3dB corner frequency is 1/CERE, then by H2(jω). Since in the vicinity of oscillation frequency, the parallel RLC tank impedance is dominated by R, |H2(jω)| can be approximated by 1 / 1 + (ωCπ rb / Rg m ) 2 , which is also a lowpass filter. Hence, the effects of the noise introduced by RE is alleviated. Another effect of this topology is that the noise shaping function is modified. Let’s consider the noise introduced by R. Again we assume that at the frequency range of interest, only R is important. Since the negative impedance without and with
and C values used yield an oscillation frequency of 1 / 2π LC = 14.53GHz, and the chosen R produces a Q factor of approximately 5 for the inductor. The simulated oscillation frequency in Figure 5 is determined where the imaginary part of the impedance is zero while the real part of the impedance remains negative. The oscillation frequency without emitter degeneration is only 9.79 GHz, which is outside of the scale of the plot in Figure 5. It is possible to have an oscillation frequency greater than 14.53GHz as shown in Figure 5. This is true for certain values of CE because of the requirement that ωLE1/ωCE be negative. Also note that without CE, the increase in RE will eventually prevent oscillation, as predicted for the nondegenerated case in section 3. The output phase noise at a 2MHz offset is given in Figure 6. Note that if CE is too small, it does not filter out the noise generated by RE, and it also increases |XEE|, which leads to a degradation in CNR. The effect on tuning range is also examined. Without emitter degeneration, when the capacitance at the collector sweeps from 600fF to 800fF, the oscillation frequency changes from 9.78 to 9.06GHz. Using the degeneration impedance of RE=300Ω and CE=250fF, the oscillation frequency changes from 14.60 to 12.90 GHz. Either in terms of the tuning range or in terms of percentage of tuning range, the degenerated oscillator exhibits superior performance over its non-degenerated counterpart. Using the simple design equations described in Section 3, several VCOs using emitter degeneration are designed and simulated. The first design contains two VCOs, one emitter degenerated and the other without degeneration, for comparison. The layouts of the two VCOs differ only in the degeneration impedances, and including output buffers they each consumes 430 um x 225 um chip area. The power and ground for the two VCOs are separated to avoid signal coupling. The power consumption for the VCO core and buffers are 27mW and 50mW, respectively. For the degenerated VCO, the simulated tuning range is 26.2 to 27.09 GHz, the phase noise at a 2MHz offset is 96.4 dBC/Hz, compared to 15.68 to 16.08 GHz and -89.6 dBC/Hz for the nondegenerated case.
The second example can be used in wired optical line applications such as SONET192. Simulation results reveal that the oscillation frequency ranges from 10.2 to 10.9 GHz, the phase noise is –101dB at a 1MHz offset, and the power consumption is 31mW including the output buffers. Its nondegenerated counterpart does not oscillate because the negative impedance is dominated by sLE rather than gm.
RE=50
RE=100 RE=150 14.0
RE=200 RE=300
5. CONCLUSIONS
RE=400
13.5
RE=500 RE=600 13.0
12.5
From an intuitive viewpoint, this paper analyzes the use of emitter degeneration to increase the oscillation frequency, tuning range and CNR of an LC oscillator. Design equations are provided that give reasonable prediction of circuit performance as verified by simulation and later, experimentally.
12.0
11.5 0
6. ACKNOWLEDGEMENT The authors would like to express their gratitude to IBM Microelectronics for support of this research.
RE=75
14.5
Oscillation Frequency (GHz)
The third design example is targeted for wireless applications around 2.1GHz. The emitter degenerated VCO oscillates from 2.14 to 2.37 GHz, exhibits a phase noise of –118dB at a 1MHz offset, and consumes 15mW. Without emitter degeneration, it oscillates from 1.65 to 1.77GHz, and its phase noise is –116.7dB at 1MHz while consuming the same power. It is also interesting to note that the amplitude of the oscillation signal is 840 and 750 mV peak to peak for the degenerated and non-degenerated VCOs. The reason why the former oscillates at a higher frequency at larger oscillation amplitudes is given in Section 3.
No degeneration, 9.79GHz RE=25
15.0
200
400
600
800
1000
1200
Degeneration Capacitance (fF)
Figure 5 Plot of oscillation frequency as a function of degeneration capacitance.
7. REFERENCES -90.00 0
200
400
600
800
1000
RE=0 RE=25 RE=50 RE=75
-94.00
RE=100 RE=150 RE=200 RE=300 RE=400
-98.00
RE=500
Phase Noise (dB)
[1] D. B. Leeson, “A Simple Model of Feedback Oscillator Noise Spectrum,” in Proc. IEEE, vol. 54, Feb. 1966, pp.329330. [2] T. H. Lee and J. F. Bulzacchelli, “A 155-MHz clock recovery delay-and phase-locked loop,” IEEE J. Solid-State Circuits, vol. 27, pp. 1736-1746, Dec. 1992. [3] W.Z. Chen and J. T. Wu, “A 2-V 2-GHz BJT Variable Frequency Oscillator,” IEEE J. Solid-State Circuits, vol. 33, pp. 1406-1410, Sep. 1998. [4] Johan D. van der Tang, Dieter Kasperkovitz and Arthur van Roermund, “A 9.8-11.5GHz Quadrature Ring Oscillator for Optical Receivers,” IEEE J. Solid-State Circuits, vol. 37, pp. 438-442, Mar. 2002. [5] A. Hajimiri and T. H. Lee, “A General Theory of Phase Noise in Electrical Oscillators,” IEEE J. Solid-State Circuits, vol. 33, pp. 179-194, Feb. 1998. [6] A. Hajimiri and T. H. Lee, “Oscillator Phase Noise: A Tutorial,” IEEE J. Solid-State Circuits, vol. 33, pp. 326-336, Mar. 2000.
RE=600
-102.00
-106.00
-110.00 Degenerated Cap (fF)
Figure 6 Simulated phase noise.
1200
