Multi-stage RF Amplifier

The multi-stage RF amplifier follows the LNA (Fig. 4.2). The LNA provides a gain of 15 dB and the remaining gain is to be achieved by the multi-stage RF amplifier.

The employed multi-stage RF amplifier is a cascade of ‘n’ identical and equal gain stages². Each gain stage is an inverter-based amplifier with a RLC resonant load. The inverter-based amplifier shown in Fig. 4.8 is the most suitable amplifier structure for gain stages of the multi-stage RF amplifier [342].

Each inverter-based amplifier stage (Fig. 4.8) provides a gain of 2.52 V/V (= 8 dB) as shown in Fig. 4.9:

Gainper stage= 8 dB (4.13)

Hence using (4.9) and (4.10), the maximum and the minimum number of inverter-based amplifier can be found:

N o of gain stagesmax = Gain_max−Gain_{LN A}

Gain_{per stage} = 71 dB−15 dB

8 dB = 7 (4.14)

N o of gain stages_min = Gain_min−Gain_{LN A}

Gain_{per stage} = 23 dB−15 dB

8 dB = 1 (4.15)

Fig. 4.10 shows the circuit schematic of the implemented multi-stage RF amplifier with a cascade of seven gain stages followed by a single squarer. Each gain stage for RF amplification is an inverter- based amplifier with a RLC resonant load (Fig. 4.8). enRF,1, . . .,enRF,7 are the signals (Table 4.3) enabling or disabling the gain stages of the multi-stage RF amplifier. The amplified signals from the gain stages are output to a single squarer through switches controlled by digital signals en_sq,1, . . ., en_sq,7 (Table 4.3).

At the lowest gain setting, the signal is amplified by the first gain stage providing a gain of

2The most energy-efficient way of designing the multi-stage RF amplifier is by cascading equal gain stages [357]. In case of equal gain stages, with the increase of the number of gain stages, the total gain increases exponentially but the power consumption increases linearly. However, in case of unequal gain stages, both the gain and power consumption increases exponentially [357].

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Table 4.3: Digital Settings of the Multi-stage RF Amplifier with seven equal gain stages: Gainper stage= 8 dB

Gain Stages Digital Signals

On/Off States

Required Gain from Multi-stage RF amplifier 8 dB 16 dB 24 dB 32 dB 40 dB 48 dB 56 dB Stage1

enRF,1 ✓ ✗ ✗ ✗ ✗ ✗ ✗

ensq,1 ✓ ✗ ✗ ✗ ✗ ✗ ✗

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ensq,2 ✗ ✓ ✗ ✗ ✗ ✗ ✗

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ensq,3 ✗ ✗ ✓ ✗ ✗ ✗ ✗

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ensq,4 ✗ ✗ ✗ ✓ ✗ ✗ ✗

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ensq,5 ✗ ✗ ✗ ✗ ✓ ✗ ✗

Stage6

en_RF,6 ✓ ✓ ✓ ✓ ✓ ✓ ✗

ensq,6 ✗ ✗ ✗ ✗ ✗ ✓ ✗

Stage7 enRF,7 ✓ ✓ ✓ ✓ ✓ ✓ ✓

en_sq,7 ✗ ✗ ✗ ✗ ✗ ✗ ✓

✓: Closes the switch;✗: Opens the switch

Gain_min= 8 dB and output to the squarer. At the highest gain setting, the signal is amplified by all the seven stages providing maximum amplification of Gainmax= 56 dB and then fed to squarer.

Hence the multi-stage RF amplifier supports gain scalability fromGainmin= 8 dB to Gainmax= 56 dB by a multiple ofGain_{per stage}= 8 dB.

The frequency response of a cascade of the LNA and the multi-stage RF amplifier (N o of gain stages

= 1, 2,. . ., 6, 7) is shown in Fig. 4.11, Fig. 4.12, Fig. 4.13, Fig. 4.14, Fig. 4.15, Fig. 4.16 and Fig.

4.17. It can be observed from Fig. 4.17 that the maximum single-ended gain obtained isGain_overall= 3306.7 V/V (= 70.4 dB) for a BW−3dB,overall= 544 MHz. The overall bandwidth BW−3dB,overall= 544 MHz is close to the normalized gain spectrum (Fig. 4.4(b)).

Discussions

It is observed that in 180 nm technology (technology employed in this work) the inverter-based amplifier exhibits a -3 dB cut-off frequency at around 1.5∼2 GHz (Appendix B.1). Thus it may be inferred that an inverter-based amplifier with a resonant load at f_c ∼ 4 GHz will display a skewed bandpass characteristic with a much reduced gain. Hence it was felt that an advanced technology should be explored. Appendix B.2 gives a design of the RF front-end (LNA and Multi-stage RF amplifier) in 65 nm technology. Though the basic amplifier in 65 nm technology has a wider frequency response, it is seen that there is no significant improvement in the overall response of the RF stage and requires around the same number of stages of RF amplification.

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