Herminio Martinez
EDN
One of the most popular circuits for amplitude control in oscillators is the softlimiter circuit (Figure 1a). When the output voltage, V_{OUT}(t), is small, diodes D_{1 }and D_{2} are off. Thus, all of the input current, V_{IN}(t)/R_{1}, flows through the feedback resistor, R_{2}, and the output voltage is:
This portion is the linear part of the limitertransfer characteristic in Figure 1b with slope of –(R_{2}/R_{1}).


Figure 1.  Diodes in the feedback circuit form the basis of this soft limiter (a). The transfer characteristic of the limiter circuit shows inflection points when the diodes begin to conduct (b). 
On the other hand, when V_{OUT}(t) goes positive, V_{A} becomes more positive, thus keeping D_{1} off; however, V_{B} becomes less negative. Then, if you continue to decrease V_{IN}(t), you will reach a positive value of the output voltage, at which V_{B} becomes approximately 0.7 V, and diode D_{2 }conducts. Thus, the positivelimiting value at the output, V_{L+}, is:
where Vγ is the forward voltage of the diodes – approximately 0.7 V. If V_{IN}(t) decreases beyond this value, V_{OUT}(t) will increase, more current is injected into diode D_{2}, and V_{B }remains at approximately –Vγ. Thus, the current through R_{5} remains constant, and the additional diode current flows through R_{6}. Therefore, R_{6} appears, in effect, in parallel with feedback resistor R_{2}, and the incremental gain, A_{V}, ignoring the diode’s resistance, in the positivelimiting region is:
Note that, to make the slope of the transfer characteristic small in the limiting region, you should select a low value for R_{6}. You can derive the transfer characteristic for positive V_{IN}(t) or negative V_{OUT}(t) in a manner identical to that of the above description. You can easily see that, for a positive V_{IN}(t), diode D_{1} plays an identical role to the one that diode D_{2} plays for negative V_{IN}(t). So, the negativelimiting level, V_{L–}, is:
and the slope of the transfer characteristic in the negativelimiting region is:
Note that increasing R_{2} results in a higher gain in the linear region and keeps V_{L+} and V_{L– }unchanged. When you remove R_{2}, the soft limiter turns into a comparator.
Thus, the circuit of Figure 1a functions as a soft limiter, and you can independently adjust the limiting levels V_{L+} and V_{L–} by selecting the appropriate resistor values and reference voltages, ±V_{REF}. Therefore, you can use a control voltage to change these limiting levels. You can base a simple AM modulator on this configuration. The RC (resistance/capacitance) phaseshift oscillator in Figure 2 includes a soft limiter in its voltage amplifier. You can alternatively use any similar RC or LC (inductance/capacitance) oscillator. You can modify the reference voltages, V_{REF} and –V_{REF}, with the input modulating voltage, V_{M}(t). This voltage dynamically adjusts the saturation levels of the oscillator’s output. The ratio of the limiter resistors determines the output amplitude and the modulation index.
Figure 2.  Inserting the soft limiter into the feedback loop of a phaseshift oscillator enables a simple AM modulator. 
Figure 3 shows the waveforms of the modulating input, V_{M}(t), and the oscillator’s modulated output, V_{OUT}(t), with the component values of Figure 2. In this case, V_{M}(t) is a sinusoidal waveform with an amplitude equal to 3 V, and trimmer R_{9} adds a 5 V offset voltage. The circuit works in a similar way to a fourquadrant analog multiplier.


Figure 3.  The modulating input, V_{M}(t) to the circuit in Figure 2 (a) obtains the modulated output voltage, V_{OUT}(t) (b). 
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