Oscillator design for veryhigh- frequency (VHF) and ultra-high-frequency (UHF) applications has been well documented in books and journals. Most early work focused on frequency stability and, to a lesser extent, on efficiency and output signal quality. But with increasing use of advanced modulation formats in communications systems, and the growing need for oscillators with extremely low phase noise, greater design emphasis is now placed on achieving oscillator designs with low phase noise. Fortunately, with the availability of accurate phase-noise measurement equipment and improving computer-aidedengineering (CAE) tools for predicting and simulating phase-noise performance, the gap between oscillator simulations and measured results has narrowed. Still, many early oscillator design strategies were based on small-signal approaches that yielded less-than-accurate predictions for output frequency, output power, and phase noise. As an alternative, largesignal, time-domain calculations will be applied to the design of a groundedbase oscillator (rather than a Colpitts oscillator) to validate the effectiveness of this design approach. Part 1 of this three-part article series will explore the use of large-signal design techniques for a grounded-base 144-MHz oscillator.

By presenting the use of the largesignal, time-domain approach with nonlinear software simulation tools in the design of VHF/UHF groundedbased oscillators, the goals include (1) accurately predicting oscillator phase noise and deriving a set of algebraic equations for the noise calculations (many CAE tools provide incorrect answers about the phase noise) and (2) developing a set of empirical equations that will guide in the synthesis of VHF/UHF oscillators. The approach yields oscillators with the best possible combination of output power and phase noise.

As a point of reference, the traditional small-signal design approach will first be used to create an oscillator for comparison to a more optimized design developed with the novel large-signal approach. Using a mix of linear equations and one large signal parameter, the device transconductance (g_m), the important noise parameters will be calculated and validated. Finally, based on this procedure, a simple but scalable and accurate set of formulas for oscillator synthesis will be presented. The novel large-signal design principles shown here for fixed or narrowband oscillators can also be applied to broadband voltage-controlled-oscillator (VCO) design. The methodology has been shown to work well even with multi-octave-band (1:3 frequency tuning range) tunable oscillators.^20-32

The grounded base configuration (Fig. 1) is a popular circuit for VHF/UHF oscillators. It is simple and can be made with very low phase noise, since the RF voltage swing at the active-device’s collector can be close to that of the supply voltage. Oscillation is based on the principle that power from the output is fed back to the emitter. This feedback arrangement generates a negative resistance at the output, compensating for the losses of the output-tuned circuit, and starts oscillating and then stabilizing the oscillation amplitude.^1-4 A complete survey of grounded-base oscillator configurations and applications can be found in references 5 to 19.

These references include some of the more popular texts recently published on oscillators. Many of the authors have attempted to predict oscillator performance based on a set of linear calculations, including use of the Leeson model or similar methods to determine phase noise. For accurate predictions of phase noise, however, several key input parameters are needed, including the large-signal noise figure of the active device, the output power, and the operating quality factor (Q). The values of these parameters are not often known and more typically approximated (or guessed). The first successful attempts at determining the large-signal phase noise were reported in references 6 and 7. But these approaches are not useful without an accompanying CAE tool, and they don’t provide design guidelines. Another problem with the linear approach is inaccuracy in predicting the actual oscillating frequency, with predicted results at higher frequencies often differing widely from actual performance.

Well-known for his work on amplifiers, Guillermo Gonzalez recently published a text on oscillators that provides an interesting overview of design based on linear calculations and CAE tools, although his approach does not provide optimum solutions.8 To demonstrate this, his methods will first be applied to the design of a 144-MHz oscillator. The resulting circuit neither provides the best output power nor the lowest phase noise and, at high frequencies, requires capacitor values that cannot be easily realized because of parasitic effects.

Figure 1 shows the typical configuration of the grounded base oscillator circuit. This type of oscillator works effectively from about 10 to above 1000 MHz. Following the procedures of ref. 8, and the large-signal conditions of ref. 11, it is possible to analyze this oscillator circuit. Kenneth Clarke was probably the first to publish the effect of the collector current conducting angle of an oscillator, but makes no mention of the relationship of it on phase noise, as done in ref. 10.

The oscillator circuit is based on a model BFR193 silicon bipolar transistor from Infineon Technologies (www.infineon.com). Designed for low-noise, high-gain amplifiers to 2 GHz, the transistor features a transition frequency (fT) of 8 GHz for +8 VDC collectoremitter voltage and 50 mA collector current. The first step in designing the oscillator circuit for this transistor is to determine the small-signal [Y] parameters for the transistor at 144 MHz and under the operating conditions of +8.8 VDC collector-emitter voltage (Vce, 10 mA collector current (Ic), 24 µA base current (IB), and +0.64 VDC base-emitter voltage (Vbe). The 10-mA collector current was selected for stable transistor cut-off transition frequency. For more output power, a collector current of 30 mA is a better choice.

Figure 2 shows a circuit for generating the oscillator’s small-signal [Y] parameters using Ansoft Designer CAE software from Ansoft (www.ansoft.com) and the time-domain model. The process is based on the configuration shown in Fig. 3 and the following definition:

Once Ansoft Designer is armed with the circuit parameters for the oscillator circuit, it uses the [Y] matrix to generate the Y-parameters:

Y11=G₁₁ + jB₁₁= (279.08-j95.07mS (2)

Y21=G₂₁ + jB₂₁= (-271.32 + j100.77)mS (3)

Y12=G₁₂ + jB₁₂= (-1030 + j78.06) μS (4)

Y₂₂=G₂₂ + jB₂₂= (1020 + j536.14) μS (5)

Figure 4 shows a standard feedback oscillator topology using parallel circuit elements. In theory, the grounded- base configuration can be rotated into a Colpitts circuit, which is often referenced in the technical literature and based on the black-box theory (ref. 5). In terms of performance, however, it cannot be said that a mathematical rotation yields the same performance. In the case of the Colpitts oscillator, the RF voltage swing is now limited by the base-to-emitter and emitter-to-ground voltages. As a result, there is less energy stored in the circuit and, because of loading, the operational Q can be degraded for the grounded-base oscillator. For the Colpitts oscillator configuration, the collector-to-base voltage (V_cb) is about 12 V. Also, parameter Y_22cb is less than parameter Y_22ce, resulting in less loading than the grounded-base configuration. The Colpitts configuration is popular because of its simplicity and its perceived high isolation since the output power is extracted from the collector, although this is nothing more than perception due to the strong Miller effect at very high frequencies. In terms of configurations other than the Colpitts, the general time-domain approach presented here is valid not only for the Colpitts configuration but for other derivative configurations.

Conditions necessary for oscillation for the parallel feedback oscillator configuration of Fig. 4 can be described by

Yout + Y3 =>0 (6)

This condition can be expressed as:

where Y_ij (i,j = 1, 2) are the smallsignal [Y] parameters of the bipolar or FET model.

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