# 7.10: Exercises

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1. The first stage of a two-stage amplifier has a linear gain of $$16\text{ dB}$$ and output $$1\text{ dB}$$ gain compression, $$P_{1o,1\text{ dB}} = −20\text{ dBm}$$. For the second stage the linear gain is $$30\text{ dB}$$ and $$P_{2o,1\text{ dB}} = 0\text{ dBm}$$.
1. Determine the input-referred gain compression, $$P_{2i,1\text{ dB}}$$ of stage $$2$$.
2. Compare $$P_{2i,1\text{ dB}}$$ and $$P_{1o,1\text{ dB}}$$. Which stage dominates gain compression?
3. What is the amplifier’s output gain compression level, $$P^{T}_{o,1\text{ dB}}$$ considering only compression from the dominant stage.
4. Calculate $$P^{T}_{o,1\text{ dB}}$$ using the method described in Section 7.2.1.
5. Compare $$P^{T}_{o,1\text{ dB}}$$ calculated in (c) and (d) and briefly discuss any discrepancy.
2. An amplifier has two cascaded stages with linear gains of $$G_{1} = 20\text{ dB}$$ and $$G_{2} = 30\text{ dB}$$, and output-referred third-order intercepts of $$\text{OIP3}_{1} = 0\text{ dBm}$$ and $$\text{OIP3}_{2} = 20\text{ dBm}$$, respectively. What is $$\text{IIP3}$$ of the amplifier? Use the organized cascade intercept method.
3. A single-stage amplifier has a linear gain of $$16\text{ dB}$$ and an output $$1\text{ dB}$$ gain compression point of $$10\text{ dBm}$$. A communication signal with a PMEPR of $$6\text{ dB}$$ is used. What is the maximum average power of the input signal before the output suffers significant compression? This is defined at the point at which the peak signal is compressed by $$1\text{ dB}$$.
4. The first stage of a two-stage amplifier has a linear gain $$G_{1} = 30\text{ dB}$$ and an output $$1\text{ dB}$$ gain compression point $$P_{1o,1\text{ dB}} = −10\text{ dBm}$$. The second stage has a linear gain $$G_{2} = 20\text{ dB}$$ and an output $$1\text{ dB}$$ gain compression point $$P_{2o,1\text{ dB}} = 10\text{ dBm}$$. What is the output-referred $$1\text{ dB}$$ gain compression point of the cascade amplifier? [Parallels Example 7.2.1]
5. An amplifier consists of two cascaded stages. The first stage has a linear gain $$G_{1} = 30\text{ dB}$$ and an output $$1\text{ dB}$$ gain compression point $$P_{1o,1\text{ dB}} = 0.1\text{ dBm}$$. The second stage has a linear gain $$G_{2} = 20\text{ dB}$$ and an output $$1\text{ dB}$$ gain compression point $$P_{2o,1\text{ dB}} = 1\text{ dBm}$$. What is the input-referred $$1\text{ dB}$$ gain compression point of the cascade amplifier? [Parallels Example 7.2.1]
6. The stages of a two-stage amplifier have linear gains of $$G_{1}$$ and $$G_{2}$$, and output $$1\text{ dB}$$ gain compression powers of $$P_{1o,1\text{ dB}}$$ and $$P_{2o,1\text{ dB}}$$, respectively. Develop a symbolic expression for the input-referred $$1\text{ dB}$$ gain compression point of the cascade amplifier.
7. An amplifier has two stages with linear gains of $$G_{1} = 20\text{ dB}$$ and $$G_{2} = 30\text{ dB}$$, and output $$1\text{ dB}$$ gain compression powers of $$P_{1o,1\text{ dB}} = 0.1\text{ dBm}$$ and $$P_{2o,1\text{ dB}} = 1\text{ dBm}$$, respectively. What is the input-referred $$1\text{ dB}$$ gain compression power of the amplifier?
8. The first stage of a two-stage amplifier has a linear power gain of $$26\text{ dB}$$ and an output $$1\text{ dB}$$ gain compression power of $$10\text{ dBm}$$. The corresponding parameters of the second stage are $$10\text{ dB}$$ and $$13\text{ dBm}$$.
1. What is the linear power gain of the two-stage amplifier?
2. What is the output $$1\text{-dB}$$ gain compression power of the amplifier for a sinusoidal RF input signal?
3. What is the maximum average output RF power of the $$\text{64-QAM-}$$modulated signal (with a PMEPR of $$7.8\text{ dB}$$) for an undistorted output (as defined by $$1\text{-dB}$$ gain compression)?
9. The stages of a three-stage amplifier have linear gains of $$10\text{ dB},\: 20\text{ dB}$$, and $$20\text{ dB}$$ respectively, and $$1\text{ dB}$$ output gain compression levels of $$−60\text{ dBm},\: −40\text{ dBm}$$, and $$−20\text{ dBm}$$ respectively. What is the output power when the gain of the amplifier is compressed by $$1\text{ dB}$$?
10. The first stage of a two-stage amplifier has a linear power gain of $$26\text{ dB}$$, an output $$1\text{ dB}$$ gain compression power of $$10\text{ dBm}$$, and an output-referred third-order intercept point $$\text{OIP3} = 26\text{ dBm}$$. The second stage has a linear power gain of $$10\text{ dB}$$, an output $$1\text{ dB}$$ gain compression point of $$13\text{ dBm}$$, and an output-referred third-order intercept point $$\text{OIP3} = 33\text{ dBm}$$.
1. What is the linear power gain of the two-stage amplifier?
2. What is the output $$1\text{-dB}$$ gain compression power of the two-stage amplifier for a sinusoidal RF input signal?
3. What is the $$\text{OIP3}$$ of the two-stage amplifier?
4. What is the input-referred third-order intercept point, $$\text{IIP3}$$?
11. The final RF output of a cell phone has a driver amplifier followed by a power amplifier. The driver amplifier has a linear gain of $$30\text{ dB}$$ and an output-referred third-order intercept point, $$\text{OIP3}$$, of $$50\text{ dBm}$$. The power amplifier has a linear gain of $$12\text{ dB}$$ and an output-referred third-order intercept point, $$\text{OIP3}$$, of $$55\text{ dBm}$$. What is the $$\text{OIP3}$$ of the driver-power amplifier cascade?
12. A two-stage amplifier has a linear power gain of $$20\text{ dB}$$, an output $$1\text{ dB}$$ gain compression point of $$30\text{ dBm}$$, and an output-referred third-order intercept point $$\text{OIP3} = 53\text{ dBm}$$.
1. What is the power of the maximum input signal when the gain of the amplifier is compressed by $$1\text{ dB}$$?
2. What is the input-referred third-order intercept point, $$\text{IIP3}$$?
13. The first stage of a two-stage amplifier has a linear power gain of $$23\text{ dB}$$, an output $$1\text{ dB}$$ gain compression power of $$1\text{ dBm}$$, and an output-referred third-order intercept point $$\text{OIP3} = 20\text{ dBm}$$. The second stage has a linear power gain of $$10\text{ dB}$$, an output $$1\text{-dB}$$ gain compression point of $$10\text{ dBm}$$, and an output-referred third-order intercept point, $$\text{OIP3} = 30\text{ dBm}$$. The signal applied to the amplifier uses QPSK modulation with a PMEPR of $$3\text{ dB}$$.
1. What is the linear power gain in decibels of the two-stage amplifier?
2. What is the output $$1\text{-dB}$$ gain compression power, in $$\text{dBm}$$, of the two-stage amplifier?
3. What is the $$\text{OIP3}$$, in $$\text{dBm}$$, of the two-stage amplifier?
4. What is the input-referred third-order intercept point, $$\text{IIP3}_{\text{m}}$$?
5. What is the single-tone output power at $$1\text{ dB}$$ gain compression?
6. What is the maximum output RF power of the QPSK-modulated signal for an undistorted output?
14. An amplifier has two cascaded stages. The stages have linear gains of $$G_{1}$$ and $$G_{2}$$, and output-referred third-order intercepts of $$\text{OIP3}_{1}$$ and $$\text{OIP3 dBm}$$, respectively. What is $$\text{IIP3}$$ of the amplifier?
15. An amplifier has two cascaded stages with linear gains of $$G_{1} = 20\text{ dB}$$ and $$G_{2} = 30\text{ dB}$$, and output-referred third-order intercepts of $$\text{OIP3}_{1} = 0\text{ dBm}$$ and $$\text{OIP3}_{2} = 20\text{ dBm}$$, respectively. What is $$\text{IIP3}$$ of the amplifier? Use the unorganized cascade intercept method.
16. The first stage of a room-temperature two-stage amplifier with a $$100\text{ MHz}$$ bandwidth has a linear power gain of $$26\text{ dB}$$, an output $$1\text{ dB}$$ gain compression power of $$10\text{ dBm}$$, and an output-referred third-order intercept point $$\text{OIP3} = 26\text{ dBm}$$. The second stage has a linear power gain of $$6\text{ dB}$$, an output $$1\text{ dB}$$ gain compression point of $$13\text{ dBm}$$, and an $$\text{OIP3}$$ of $$33\text{ dBm}$$. The noise figure of the first stage is $$3\text{ dB}$$ and the noise figure of the second stage is $$6\text{ dB}$$. The minimum acceptable SNR, SNR$$_{\text{min}}$$, at the output of the amplifier is $$16\text{ dB}$$.
1. What is the linear power gain of the two-stage amplifier?
2. What is the output $$1\text{-dB}$$ gain compression power of the two-stage amplifier for a sinusoidal RF input signal?
3. What is the $$\text{OIP3}$$ of the two-stage amplifier?
4. What is the noise figure of the two-stage amplifier?
5. What is the noise, in $$\text{dBm}$$, applied to the input of the two-stage amplifier in a $$100\text{ MHz}$$ bandwidth is the source has a Thevenin resistor at room temperature?
6. What is the power of the noise, in $$\text{dBm}$$, in a $$100\text{ MHz}$$ bandwidth at the output of the two-stage amplifier?
7. What is the output-referred spurious free dynamic range of the two-stage amplifier in decibels?
8. What is the output-referred dynamic range of the two-stage amplifier in decibels?

## 7.10.1 Exercises By Section

$$†$$challenging, $$‡$$very challenging

$$§7.2\: 1†, 2, 3, 4, 5†, 6†, 7†, 8, 9, 10, 11†, 12†, 13†, 14, 15$$

$$§7.7\: 16†$$

## 7.10.2 Answers to Selected Exercises

1. $$-11\text{ dBm}$$
1. (e) $$5.2\text{ dBm}$$

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