The millimeter wave radio front-end is designed in UMC’s 65nm CMOS process that has an FET of around 220GHz. In order to generate and receive signals at 250GHz, a differential frequency doubling stage is used at the output (compare Section 3.3 – Active Approaches in CMOS). This stage operates at a fundamental frequency of 125GHz, producing power at 250GHz due to FET device compression.
In order to control the radiation pattern, it is desirable to control the amplitude and the phase of the generated 250GHz signal. However, doing so reliably is difficult because gain at 125GHz comes at a premium (with approximately 5dB available gain at 125GHz). With so little available gain, any modeling inaccuracy in the FETs will greatly impact the performance of even the simplest circuit blocks, making it difficult to reliably design blocks such as gain-and phase-control blocks.
Rload
Sin(t+q1+f1) Iload
Gain control can be achieved in a variety of ways. For a differential frequency doubling stage, we expect any gain reduction at the fundamental frequency to result at approximately twice the reduction at the second harmonic output if we assume that the second harmonic is produced by gain compression that can be modeled using a polynomial expression, to wit
(5-2)
A disadvantage of this approach is that it requires the input signal to be reduced, which may be impossible if an oscillator is used such that any reduction in the input signal requires a reduction in the output signal and hence may lower the loop-gain of the oscillator to below one, making it impossible for oscillations to start up.
An alternative that is used in our design is to use an outphasing approach at the second harmonic. Outphasing is traditionally used in power amplifier design [64] [65]. The advantage of this approach is that the amplitude control at the second harmonic has little effect on the circuit operation at the fundamental frequency, since the shift in loading and amplitude happens at the second harmonic. Adding the voltages of two stages in series (compare Figure 5-4), we can write the output voltage and current as
( ) ( )
(5-3)
Thus, the magnitude of the output voltage is a function of the phase difference . The magnitude of the impedance seen each of the stages is ⁄ ( ) and the angle is . Thus, by simply changing the phase-angle, we can affect the output
amplitude. Again, because the outphasing in our design is done at the second harmonic (the stages are isolated at the fundamental frequency), the mismatch effects only occur at the second harmonic and do not significantly impact the performance at the fundamental frequency.
Using the differential phase to change the overall output amplitude, we can use the common mode phase to change the overall phase of the output signal, as shown above. Thus, in order to control both the differential mode and common mode input phases to the two output stages, we need to independently control the phases of each of the input signals. There are several possible approaches to effect a phase change at RF frequencies and two of the approaches were investigated in detail for this design. In general, approaches fall into two broad categories, active and passive approaches.
Passive approaches involve electronically tunable delay elements such as transmission lines or (switched) lumped filters [66]. Purely passive approaches at RF frequencies have the advantage that their operation does not depend on active device gain, which comes at a premium at frequencies that are a sizeable fraction of the active device maximum gain frequency. However, the signal loss has to be compensated for in some fashion. They do, however, separate the function of providing phase shifts from the function of providing signal gain, and are therefore more compatible with a functional block level approach. The biggest disadvantage of passive approaches is that they frequently require a large layout area
Active approaches fall into three broad categories: active delay-based approaches [66] [68], Cartesian phase-rotation approaches [69] and locked oscillator-based
approaches [70]. In practice, the difference between a delay-based approach and a locked oscillator approach is a gradual one. An amplification stage that provides a large amount of signal delay typically exhibits an under-damped response (i.e., exhibits gain peaking), and an oscillator is, in some sense, an amplification stage that exhibits infinite gain peaking. Using an oscillator has the advantage that an oscillator can, in theory, provide full phase shift. In particular, Adler’s equation [71] can be written as
( ) (5-4)
where is the free-running frequency, is the frequency difference between locking signal and free-running frequency, is the oscillator quality factor and and are the oscillator amplitude and the locking signal amplitude. Hence, the locking range is limited to
(5-5)
If oscillators are used, their locking range thus has to encompass the entire range of desirable operating frequencies, and hence their inherent quality factor has to be low enough to allow a shallow enough phase shift gradient to be useful. Because the feasible tuning range of integrated oscillators at very high frequencies is limited, the inherent quality factor should be large enough to provide appreciable phase shift across the frequency band of interest. Furthermore, because oscillators are large signal circuits, they typically provide gain restoration, which is an advantage since we would like to keep the amplitudes of the two signals in the outphasing stages to be the same amplitude (as we have previously assumed).
Finally, since the phase-shift at the second harmonic is doubled from the phase- shift accomplished at the fundamental frequency, a single oscillator phase-shifter can theoretically provide a full phase shift at the output frequency. For a phase- shift, however, the oscillator is on the verge of being unlocked, and hence two oscillators are used in series. This lowers the locking range requirement for each oscillator to , and also alleviates input signal strength requirements.