Example 4: Miller Op-amp

As a first example of a DCA on the circuit level, we consider a two-stage Miller-compensated op-amp designed in a commercial $0.18\mathrm{\mu m}$ CMOS technology (Figure E4.1). The op-amp is placed in an inverting feedback configuration with a gain of $5$ and drives a load capacitance of $10\mathrm{pF}$, resulting in a gain-bandwidth product of $10\mathrm{MHz}$. The circuit is split into three sub-circuits: the input stage, which has three ports, the current mirror, and the output stage which both have two ports.

Figure E4.1The two-stage Miller op-amp under test.

The amplifier is excited by lowpass random-odd multisines with a base frequency $f_{0}$ of $100\mathrm{kHz}$ and $f_{\mathrm{max}}=10\mathrm{MHz}$. The RMS voltage of the multisines is set to $0.1\mathrm{V}$. The steady-state response of the circuit to $50$ different-phase multisines is obtained with HB simulation. The obtained spectrum of the output wave $B_{t}$ is shown in Figure E4.2.

Figure E4.2Output spectrum of the Miller op-amp obtained with $50$ different-phase multisines. The excited bins are shown in black, the even bins in blue and the non-excited odd bins in red. The RMS of the distortion is shown with a blue and red line for the even and odd bins respectively.

The Miller op-amp can be considered to be weakly non-linear, so the small-signal S-parameters were used to represent each sub-circuit. To test the validity of this small-signal assumption, the BLA from the reference multisine to all waves in the circuit was compared to the result obtained with an AC simulation as explained in Section Section 6. The largest difference is observed on the frequency response from the reference to the output wave of the second stage and it is shown in Figure E4.3. This difference is small enough to allow using the small-signal S-parameters instead of the MIMO BLA to represent each sub-circuit.

Figure E4.3The frequency response from input voltage to the output wave of the circuit (orange) doesn’t lie far from the corresponding BLA (green +), so the small-signal S-parameters can be used to represent the sub-circuits instead of the MIMO BLA.

The results of the DCA at four different frequencies are shown in Figure E4.4. The contributions are combined for each stage as was explained in Section Section 4.1. For three sub-circuits, this results in six distortion contributions, three direct distortion contributions (one for each stage) and three correlation distortion contributions.

Figure E4.4Distortion contributions to the output wave of the Miller op-amp at four different frequencies.

The even and odd distortion contributions can be split again because odd RPM were used. At $200\mathrm{kHz}$ (top left in Figure E4.4), we obtain only even-order non-linear contributions, since this is an even frequency line as defined by the chosen frequency grid. The input stage seems to generate the most distortion with a direct contribution which is $150\%$ of the total output distortion at that frequency bin, but its contribution is largely cancelled in its correlation with the current mirror, which has a contribution of $-120\%$ of the total distortion. This leads to the output stage as the dominant source of distortion at $200\mathrm{kHz}$. This shows the importance of the correlation between the distortion sources in the circuit. In the odd-order contributions at $300\mathrm{kHz}$ (Top right in Figure E4.4), the input stage is clearly the dominant generator of non-linear distortion.

The bottom series of plots in Figure E4.4 shows the results at the high-frequency end of the analysed band. At $9.8\mathrm{MHz}$, the output stage dominates the even-order contributions. At $9.9\mathrm{MHz}$, the odd contribution of the output stage ($350\%$) is compensated with a covariance with the input stage ($-350\%$), making the input stage the dominant source of distortion at this particular frequency.

With this example, we have shown that the BLA-based DCA can be used in circuit-level simulations to obtain the distortion contributions. Taking the correlation between distortion sources of different sub-circuits into account is crucial to obtain an accurate representation of the circuit’s distortion.