Design of a
Voltage Controlled
Oscillator (VCO) based on a Ring Oscillator Topology with Differential
Elements
2.2 Design of a VCO Based on Ring Oscillator Topology
Using Starved-Current Elements.
Figure 2.2.1 presents the schematic of a VCO based on ring
oscillator topology using five starved-current elements. The
transistors M1, M2, M11 and M16 represent one delay element of the ring
oscillator. Transistors M2 and M11 operate as an inverter and M1 and
M16 operate as current sources. The current sources, M1 and M16 limit
the current available to the inverter, M2 and M11. The drain currents
in M0 and M21 are the same and are controlled by
the input control voltage Vc. The currents in M0
and M21 are mirrored in each inverter/current source stage.
Figure 2.2.1 A VCO
using five starved-current elements.
Design
equations
Figure 2.2.2 presents
the simplified schematic of one stage of the VCO. The total capacitance
on the drains of M2 and M11 can be expressed as:
Ctot = Cout + Cin
(2.2.1)
Figure 2.2.2
Simplified model of a single stage of the VCO.
For a minimum size
inverter the value of Ctot can be expressed as:
Ctot = Cox L (Wp +Wn)
+ 2Cdbp +2Cgdp + Cdbn +2Cgdn
= Cox L (Wp +Wn) +
2[WpLsCjp+(2Ls+Wp)Cjswp] + 2CgdopWp + [WnLsCjn+(2Ls+Wn)Cjswn]+
2CgdnoWn
Ctot = 2.0389 + 8.198
= 10.298 fF
Knowing the value of Ctot and the number of stages N, the center
frequency of the current-starved VCO can be estimated using equation
2.2.2 [Jacob], for the particular case when Id = Idcenter
(current when
control voltage is Vdd/2).
fout = Id/(N Ctot
Vdd)
(2.2.2)
The maximum
oscillation frequency is determined by finding Id
when the control voltage is Vdd.
Design
Example
Suppose that we
wanted to design a VCO using five starved-current elements, with a fout
=1.0 GHz, the current needed to generate this oscillation is:
Id = fosc N Vdd Ctot
= kn’ (W/L) [(Vgs-Vtn)Vdsat-Vdsat^2/2]
From last expression,
the size of transistor M21 can be calculated using the following
expression:
Wn= (fosc
N Vdd Ctot L) / (kn’[(Vgs-Vtn)Vdsat-Vdsat^2/2])
=
(1 G)5 (2.5) (10.3 f) (0.24 u)/ (116E-6[(1.25-0.46)0.6-0.6^2/2])
= 0.84 um
Using a value of Wn=0.9 um, the schematic of the VCO with five
starved-current elements is presented in figure 2.2.1 Figure 2.2.3
presents the output frequency fout as function of the control voltage
Vc.
Figure 2.2.3 fout as a function
of Vc
fout was estimated using the Fast Fouried Transform (FFT) from
HSPICE. From this plot it is observed that, in general fout is not a
linear function of Vc. However, we can set a region where fout is a
linear function of Vc. For example, from Vc = 1.8 V to 2.5 V fout is a
linear function of its control voltage Vc. Due to that, the tuning
sensitivity (change in output frequency per unit
change in the control voltage) of this VCO can be given as a minimum
and maximum value or give several values. For example, there
exist a tuning sensitivity of 65 MHz/V if Vc changes from 1.8 V to 2.5
V, a tuning sensitivity of 325 MHz/V if Vc changes from 1.2 V to 1.6 V
and a sensitivity of 1123 MHz/V if Vc changes from 0.8 V to 1.2 V.
The time domain of the VCO-output when Vc= 1V is presented in
figures 2.2.4. Moreover, the spetrum of the oscillator for Vc=
1.0 V and Vc= 2.5 V is presented in figure 2.2.5 and 2.2.6,
respectively.
Figure 2.2.4 Time domain response of
VCO output, when Vc= 1.0 V
Figure 2.2.5 Frequency domain response
of VCO output, when Vc= 1.0 V
Figure 2.2.6 Frequency domain response
of VCO output, when Vc= 2.5 V
