Example 1: BLA of a Miller op-amp in feedback

Before we use the BLA in a DCA, let us illustrate how the BLA is used to describe the behaviour of an op-amp placed in a negative feedback configuration as shown in Figure E1.1.

Figure E1.1 The op-amp under test is a two-stage Miller op-amp designed in a commercial $0.18\mathrm{\mu m}$ technology with a Gain-Bandwidth product of $10\mathrm{MHz}$ for a load capacitance of $10\mathrm{pF}$.

The reference signals are lowpass random-odd RPM (2.3) with $f_{0}=f_{\mathrm{min}}=0.1\mathrm{kHz}$ and $f_{\mathrm{max}}=100\mathrm{kHz}$ (Figure E1.2). The amplitude of the multisines is chosen flat as a function of frequency and such that the RMS voltage equals $50\mathrm{mV}$.

Figure E1.2 Spectrum of the reference signal.

The input and output voltages obtained with a Harmonic Balance (HB) simulation clearly contain non-linear distortion (Figure E1.3), as there is energy appearing at non-excited frequency lines. Even-order distortion (blue) and odd-order distortion (red) are separated by using the odd multisines. The in-band odd non-linear distortion is visible on the detection lines. The BLA obtained with $7$ different-phase multisines is shown in Figure E1.4. A compression of $0.1\mathrm{dB}$ is observed with respect to the results obtained with an AC simulation.

Figure E1.3 Spectra of the signals at the input and output of the op-amp.

Figure E1.4 Obtained BLA and its uncertainty $\sigma_{BLA}$. Due to compression, the BLA differs from the linearised response $G_{AC}$ obtained with an AC simulation.