Subsections

• 6.4.1 Amplifier
• 6.4.2 Amplifier with Resonant Circuit
• 6.4.3 Colpitts Oscillator Circuit

6.4 Oscillator

Figure 6.10: The three subcircuits which are used in the example circuits are shown on the left side. They are parts of the three circuits depicted on the right [231].

This example demonstrates the implemented mixed-mode AC features on the simulation of a Colpitts oscillator and two intermediate circuits. The following three circuits are simulated by means of transient and small-signal device/circuit simulation:

1. An amplifier with one active device.
   
2. A resonant circuit is coupled to the output of the amplifier.
   
3. The oscillator is eventually constructed by feeding back the output of the resonant circuit to the input of the amplifier.

Since all three circuits consist of equal subcircuits (see Figure 6.10), the input-deck inheritance feature can be perfectly used, see Appendix A.13 for more details on this.

6.4.1 Amplifier

The amplifier circuit is a combination of the core and the AC source subcircuits as well as of load elements. The transistor used in the core subcircuit is a $0.4\times12\mathrm{\mu m^2}$ SiGe-HBT device structure obtained by process simulation [110]. The structure was thoroughly investigated by steady-state and small-signal AC simulations [233] as presented in Section 6.2.

CircuitAmplifier
{
   Vsrc : ~SubCircuits.Vsrc { in  = "pin1"; }
   Core : ~SubCircuits.Core { in  = "pin1"; 
                              out = "pin2"; }

   CL : ~Devices.C { N1 = "pin2"; N2 = "pin3"; C = 1 nF; }
   RL : ~Devices.R { N1 = "pin3"; N2 = "gnd";  R = 1e3;  }
}

All simulations use the mixed-mode iteration scheme (see Section 3.6.4). In the first block the fixed node voltages apply static boundary conditions at the transistor terminals in order to improve convergence to an initial solution useful for the subsequent circuit simulations. In this case, the three fixed node voltages ( $V_\mathrm{pin2}=$2.0$\,$V, $V_\mathrm{pinB}=$1.2$\,$V, and $V_\mathrm{pinE}=$0.4$\,$V) represent the dimensioning of the circuit in respect to the chosen operating point. Transient simulation results are shown in Figure 6.11. The linear equation system has a dimension of 11,601 and the simulator requires between 1.0 and 2.9$\,$s per time step on a 2.4$\,$GHz Intel Pentium IV with 1$\,$GB memory running under Suse Linux 8.2.

Figure 6.11: Result of transient simulation of the amplifier circuit with $V_\textrm {ac}=10\$mV and $f = 2.4\$GHz [231].
Figure 6.12: Results of small-signal simulations of the resonant circuit: absolute value (left) and argument (right). The results are compared with ADS simulations using a VBIC95 model of a similar transistor [231].

6.4.2 Amplifier with Resonant Circuit

The second example circuit consists of all three subcircuits, since the resonant circuit is now coupled to the output of the amplifier. The resonant circuit is configured for an oscillation frequency of 10$\,$GHz. This can be confirmed by results of a small-signal simulation as shown in Figure 6.12 ( $V_\mathrm{ac}=$1$\,$mV). In average, MINIMOS-NT requires 8.5$\,$s per frequency step. With a VBIC95 compact model of a similar transistor, the circuit simulator was used to obtain data from the same circuit.

CircuitResonant
{
   Core : ~BaseCircuits.Core { in = "pin8"; out = "pin4"; }
   Vsrc : ~BaseCircuits.Vsrc { in = "pin8"; }
   LC   : ~BaseCircuits.LC   { in = "pin4"; out = "pin9"; }

   R5   : ~Devices.R         { N1 = "pin9"; N2 = "gnd"; R  = 1e3; }
}

6.4.3 Colpitts Oscillator Circuit

Finally, a Colpitts oscillator circuit is built by feeding back the output of the resonant circuits to the input of the core circuit (amplifier).

CircuitOscillator
{
   Core : ~SubCircuits.Core { in  = "pin1"; out = "pin2"; }
   LC   : ~SubCircuits.LC   { in  = "pin2"; out = "pin1"; }
}

Figure 6.13: Result of the transient simulation of the oscillator: output $V_\textrm {pin2}$ in the initial phase (left) and in the state of equilibrium (right) [231].

At turn on, random noise is generated within the active device, which is here the SiGe bipolar junction transistor, and then amplified. This noise is positively fed back through the frequency selective circuit (resonant circuit consisting of an inductor and two capacitors) to the input, where it is amplified again. After the initial phase, a state of equilibrium is reached, where the losses are compensated by the power supply. The amount of feedback to sustain oscillation is basically determined by the $C_\mathrm{1a}/C_\mathrm{1b}$ ratio.

Transient simulation results are shown in Figure 6.13. In the simulator, the random noise of the active device is replaced by a numerical noise caused by the restricted representation of floating point numbers. The simulator requires 0.4$\,$s in the initial phase and between 1.9$\,$s and 2.9$\,$s in the state of equilibrium per time step.