Waveform shaping and output harmonic current

To quantify the improvement in harmonic content of the output current, we first study the current waveform and the magnitude of harmonic current generated by a conventional frequency tripler. All simulations in this sections are run for extracted device models for the device layout shown in Fig. 4.13 in Section 4.2. The amplitude of the input sinusoid is constrained by the 2Vdd (3 V in

130 nm CMOS as Vdd = 1.5 V) limit on the voltage swing between any two device nodes for long

term reliability. The clipped sine wave output current for VGS,DC = 0 V is shown in Fig. 4.2(b) for a

maximum input amplitude of Vdd (limited by the gate-drain 2Vdd limit on the negative half swing).

The third harmonic current generated by a 24 × 2 µm/120 nm device in 130 nm CMOS for different input amplitudes across gate bias is shown in Fig. 4.3(a). This device size is the same as that used for the implemented power mixer prototype of Section 4.2. The multiphase implementation

Figure 4.3: Third harmonic current generated by a device when it is configured as (a) frequency tripler (the dashed portion of a curve indicates when the input amplitude violates long-term relia- bility guidelines), and (b) power mixer.

of the tripler requires that each of the three devices is 8 × 2 µm/120 nm. The dashed portion of a curve indicates when the input amplitude causes either the gate-source or gate-drain swing to exceed the 2Vdd limit on either the positive half swing or the negative half swing respectively. We

see a maximum of 3.4 mA for VGS,DC = 1.5 V at Aω= 1.5 V.

The waveforms for a power mixer for two different relative phase shifts, φ = 0◦ and φ = 90◦, are shown in Fig. 4.4. For simplicity, in this work we have chosen gate and source bias voltages of 0 V. The 1 : 2 frequency ratio between the input harmonics implies that we only need to consider relative phase shifts between 0◦ and 180◦. The input amplitudes are set to Aω= 1.5 V and A2ω = 1.5 V for

both cases. The second harmonic swing at the gate node is limited by the gate-drain breakdown and the fundamental swing at the source node is limited by the drain-source breakdown. It is confirmed that for these amplitudes the gate-source waveform also does not violate the condition for long term reliability for any φ between 0◦ and 180◦. For φ = 90◦, the current waveform has almost the same peak as the tripler current waveform in Fig. 4.2(b) but appears to have a richer nonlinearity content. For φ = 0◦, the clipped current waveform is similar in shape to the conventional frequency tripler but has more than twice the peak current in Fig. 4.2(b).

CHAPTER 4. THZ POWER GENERATION:POWER MIXERS 56

Figure 4.4: Gate-source voltage shape and the resultant output current waveforms for the power mixer with Aω= A2ω = Vdd = 1.5 V and a relative phase shift φ of (a) 90◦, (b) 0◦.

in Fig. 4.3(b). For A2ω = 1.5 V and Aω = 1.5 V and a relative phase shift of 0◦, the 24×2 µm/120 nm

device generates 13.3 mA third harmonic current. This is four times higher than the maximum third harmonic current of the frequency tripler. If the output load is still determined by the substrate loss mechanism, the power mixer can deliver 16× higher output power at the third harmonic than the conventional frequency tripler. However, it is challenging to generate such a large voltage swing at the second harmonic, and hence large second harmonic power, even at the device gate node. Fig. 4.3(b) shows the resultant third harmonic current for reduced second harmonic swing as well. Even at half-swing with A2ω = 0.7 V, the maximum third harmonic current of 8.2 mA is 2.5× higher

than the frequency tripler, which is a 7.5 dB improvement in output power.

The improvement in the third harmonic current (i3ω) can be quantified by studying the peak

of the current waveform, ipeak, and the ratio of third harmonic current to the peak of the current

waveform, F3 = i3ω/ipeak. F3 is an intuitive measure of the desired nonlinearity in the waveform.

i3ω can therefore be increased by either increasing ipeak or F3, or both.

In a frequency tripler, clipping of the sinusoidal current generates the desired harmonic content. For the same amplitude, at low bias, the waveform is more clipped and can have higher harmonic

Figure 4.5: Ratio of third harmonic current to peak current, F3 = _ipeaki3ω , generated by a device

when it is configured as (a) a frequency tripler, and (b) a power mixer (Aω= 1.5 V).

Figure 4.6: Peak of output current waveform, ipeak, generated by a device when it is configured as

(a) a frequency tripler, and (b) a power mixer (Aω= 1.5 V).

content. This is seen in Fig. 4.5(a) where F3 is consistently largest for a 0 V gate bias across

different input amplitudes. It peaks to a maximum of 0.17 for a 0 V bias and Aω = 0.5 V. As the

gate bias increases far beyond the threshold voltage of the device, for a given amplitude, there is less clipping and the output waveform is increasingly more sinusoidal with a lower F3. For example, for

VGS,DC = 1.5 V and Aω = 1.5V the nonlinearity measure F3 is only 0.04. However, at this high

bias and amplitude, the ipeak at 74.7 mA is much higher (Fig. 4.6(a)). The higher ipeak dominates

improvement in third harmonic current so that at Aω = 1.5 V and VGS,DC = 1.5 V, the tripler

yields 3.4 mA compared to only 0.3 mA for VGS,DC = 0 V and Aω = 0.5 V.

For the power mixer, the maximum ipeak is 85 mA and it appears for Aω= 1.5 V, A2ω = 1.5 V

and φ = 0◦ (Fig. 4.6(b)). We recall from Fig. 4.4(b) that a relative phase of φ = 0◦ results in a much higher peak current but a waveform shape similar to that generated by a frequency tripler

CHAPTER 4. THZ POWER GENERATION:POWER MIXERS 58

Figure 4.7: Output power delivered to the optimal 30 Ω load by the device as a (a) frequency tripler, (and b) power mixer with Aω = 1.5 V.

when at a low (0V) bias voltage. Indeed, F3 = 0.16 at this point (Fig. 4.5(b)) is comparable to

the peak F3 = 0.17 for a 0 V bias tripler. However, the ipeak of 85 mA is significantly higher and

comparable to the maximum ipeak of the frequency tripler. Consequently, the net third harmonic

current generated is 13.3 mA, significantly higher than the frequency tripler. For a relative phase shift of φ = 90◦, we observed in Fig. 4.4(a) that the ipeak is lower than the φ = 0◦ case but the

waveform appears to have significantly higher nonlinear content. This is seen in Fig. 4.5(b) and Fig. 4.6(b) where ipeak has fallen to 42.6 mA, about half its value at φ = 0◦, and F3 is two times

higher at 0.33. As such, an i3ω of about 13 mA for A2ω = Aω = 1.5 V is seen at both φ = 0◦ and

φ = 90◦. While there is a trade off between ipeak and F3 in both circuit configurations, the power

mixer outperforms the tripler substantially by exploiting device nonlinearity more effectively to generate higher third harmonic current.