R-L-C Feedback Technique

The R-L-C negative feedback technique is adopted in this work for compensating the gain at high frequencies and producing a positive gain slope. The feedback resistor (Rf), feedback capacitor (Cf) and feedback inductor (Lf) are connected in series. Fig.

2.17 shows the circuit schematic and equivalent small-signal model of the transistor with the R-L-C feedback. The principle of this technique is that the feedback inductor (Lf) provides large inductance to resonate the gate-to-drain intrinsic capacitor (Cgd) of the transistor and increases the reverse isolation of the transistor. The poor reverse isolation degrades the performance of the maximum gain and destabilizes the transistor.

The reverse isolation directly affects the S12 of the transistor. Cgd can be resonated by selecting the Lf inductor in parallel with Cgd. Therefore, maximum gain and stability will be improved apparently. The feedback capacitor (Cf) is used to block DC current between the drain and the gate of transistors. Through R-L-C feedback, the gain is boosted at high frequencies and reduced at low frequencies which can improve the flatness of the overall bandwidth and make the bandwidth wider.

Fig. 2.17 The circuit schematic and equivalent small-signal model of the transistor with the R-L-C feedback technique.

In order to explain the main concept, the circuit is temporarily simplified, and the effects of Cf and Rf are ignored. Therefore, the circuit schematic and equivalent small-signal model of the transistor with only Lf and ideal DC block are shown in Fig.

2.18. The ideal blocking capacitor is just used to separate DC level between the drain and the gate of transistors. Fig. 2.19 shows the maximum gain and stability factor of the transistor with different Lf at 6 GHz. When Lf is 3 nH, the peak maximum gain of transistor appears. According to the simulation, the maximum gain of the transistors with Lf is 8-dB higher than the transistors without Lf. The stability factor is about unity.

Fig. 2.20 shows the maximum gain of the transistor of 4 fingers and 50-μm gate width at different Lf value. At each resonant frequency, the maximum gain of each curve is larger than the original. By using a feedback inductor, the maximum gain of the transistor is effectively reduced in the lower frequency. The maximum gain at 4 GHz is reduced by approximately 10 dB with 3.5-nH Lf. Moreover, the resonant frequency becomes lower as the Lf increases. The Lf can be adjusted and optimized for the required maximum gain and gain slope. If Lf approach infinity and maximum gain curve will be the same as the original maximum gain curve, this is a special case.

Fig. 2.18 The circuit schematic and equivalent small-signal model with L^f.

0 1 2 3 4 5 Maximum Gain) Stability Factor

Fig. 2.19 The maximum gain and stability factor of the transistor of 4 fingers 25-μm gate width versus feedback inductance Lf at 6 GHz.

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Fig. 2.20 The maximum gain of the transistor of 4 fingers and 25-μm gate width at different Lf value.

The R-L-C feedback technique with only feedback inductance Lf has been discussed above. However, the impact of other components still needs to be taken into consideration, and there is no ideal blocking capacitor in reality. Therefore, a non-ideal feedback capacitor Cf is added to the circuit. The circuit schematic and equivalent small-signal model of the transistor with Lf and Cf are shown in Fig. 2.21. Fig. 2.22 and Fig. 2.23 show the maximum gain and stability factor of the transistor of 4-fingers and 50-μm gate width with 3.5-nH Lf and different Cf. The resonator consisting of Lf and Cgd

fixes the maximum gain point at 12 GHz. The original maximum gain curve is also shown together to compare the simulated results. Compared with the curve with ideal Cf, the stability factor curve at the resonance frequency is also improved. As the Cf

capacitance decreases, the local minimum frequency becomes higher. A precipitous positive gain slope is obtained by selecting the Cf value. In this case, the local minimum point is fixed around 2 GHz with 1-pF Cf and the gain slope is about 2-dB per GHz.

Fig. 2.21 The circuit schematic and equivalent small-signal model with Lf and CF.

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Fig. 2.22 The maximum gain of the transistor of 4-fingers 200-μm total gate width with 3.5-nH Lf and different Cf.

Fig. 2.23 The stability factor of the transistor of 4-fingers 200-μm total gate width with 3.5-nH L and different C.

Last but not least, the Rf is merged into the total circuit of the R-L-C feedback technique. Fig. 2.24 shows maximum gain of the transistor of 4 fingers and 50-μm gate width with feedback components which contains 3.5-nH Lf, 1-pF Cf and different Rf. Generally, in unconditional stability, the amplifier may be stable without Rf. However, it is difficult to implement the transistor with unconditional stability. Therefore, the Rf is usually required. Rf not only improves the stability but also changes the maximum gain slope. The maximum gain response of this transistor will be flatter with 250 Ω feedback resistance. In addition, as the Rf increases, the stability is improved also. Fig. 2.25 shows stability factor of the transistor of 4 fingers and 50-μm gate width with feedback components which contains 3.5-nH Lf, 1-pF Cf and different Rf. Finally, the gain slope of each stage is simulated by using the ideal components to achieve the wideband gain compensation. Fig. 2.26 shows the pre-simulation of the concept of gain slope with each stage. As the result, the overall bandwidth is wider.

5 10 15 20 feedback components which contains 3.5-nH Lf, 1-pF Cf and different Rf.

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Fig. 2.25 The stability factor of the transistor of 4 fingers 200-μm total gate width with feedback components which contains 3.5-nH Lf, 1-pF Cf and different Rf.

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Fig. 2.26 The pre-simulation of the concept of gain slope with each stage.