PE ECC Practice Problems with Worked Solutions

The PE Electrical and Computer: Electronics, Controls, and Communications exam is separate from PE Electrical and Computer: Computer Engineering. ECC questions lean into analog and digital circuits, instrumentation, controls, signal processing, RF/fiber/communications, noise, and reliability. The best practice problems make you decide which reference lane applies before you start arithmetic.

How to Use These PE ECC Practice Problems

Work each problem in three passes: first identify the official topic lane, then write the governing model, then calculate. If a problem provides a compact table or relationship, treat it like a practice substitute for the exam-day electronic reference: it gives enough information to solve without copying a handbook page or hiding a required standard.

PE ECC Practice Problems

1. Inverting Summing Amplifier

An inverting summing amplifier has \(R_f = 50\,k\Omega\). Input \(V_1 = 0.80\,V\) is applied through \(R_1 = 20\,k\Omega\), and input \(V_2 = -0.30\,V\) is applied through \(R_2 = 10\,k\Omega\). The output voltage is most nearly:

1. -0.50 V
2. +0.50 V
3. -2.5 V
4. +2.5 V

Solution

For an inverting summer, \(V_{out}=-R_f(V_1/R_1+V_2/R_2)\). The bracketed term is \(0.80/20k + (-0.30)/10k = 40\,\mu A - 30\,\mu A = 10\,\mu A\). Multiplying by \(50k\Omega\) gives \(0.50\,V\), then the inverting sign gives -0.50 V. Reference lane: Electronics Circuits > operational amplifiers.

2. Quarter-Bridge Instrumentation Signal

A quarter-bridge strain gage uses \(V_s = 5.0\,V\), gage factor 2.1, and strain \(850\,\mu\varepsilon\). For small strain, use \(V_o \approx V_s(GF\varepsilon/4)\). The bridge output is most nearly:

1. 0.45 mV
2. 1.1 mV
3. 2.2 mV
4. 8.9 mV

Solution

Convert strain: \(850\,\mu\varepsilon=850\times10^{-6}\). Then \(V_o=5.0(2.1)(850\times10^{-6})/4=0.00223\,V=2.23\,mV\). The nearest answer is 2.2 mV. Reference lane: Measurement and Instrumentation > bridge sensors and signal conditioning.

3. Reliability From FIT Rate

A component has a constant failure rate of 250 FIT. Using \(1\) FIT \(=10^{-9}\) failures/hour, the MTBF is most nearly:

1. 250,000 h
2. 1,000,000 h
3. 2,500,000 h
4. 4,000,000 h

Solution

The failure rate is \(\lambda=250\times10^{-9}\,h^{-1}=2.50\times10^{-7}\,h^{-1}\). MTBF is \(1/\lambda=4.0\times10^6\,h\). Answer: 4,000,000 h. Reference lane: Safety and Reliability > failure rate and MTBF.

4. FIR Filter Sample

A short FIR filter has \(h[0]=1.00\), \(h[1]=-0.50\), and \(h[2]=0.25\). The input samples are \(x[0]=2\), \(x[1]=4\), and \(x[2]=1\). Using \(y[2]=h[0]x[2]+h[1]x[1]+h[2]x[0]\), \(y[2]\) is:

1. -1.5
2. -0.5
3. 0.5
4. 3.0

Solution

\(y[2]=1(1)+(-0.50)(4)+0.25(2)=1-2+0.5=-0.5\). Answer: -0.5. Reference lane: Signal Processing > convolution and FIR filters.

5. Digital Setup Slack

A register-to-register path has a 10.0 ns clock period, 1.2 ns clock-to-Q delay, 5.6 ns combinational delay, 1.0 ns routing delay, and 0.8 ns setup time. The setup slack is most nearly:

1. 0.6 ns
2. 1.4 ns
3. 2.2 ns
4. 4.4 ns

Solution

Required path time is \(1.2+5.6+1.0+0.8=8.6\,ns\). Slack is \(10.0-8.6=1.4\,ns\). Answer: 1.4 ns. Reference lane: Digital Systems > sequential timing.

6. Fiber Telemetry Link Budget

A fiber telemetry link has launch power \(-3\,dBm\), fiber attenuation \(6\,dB\), connector/splice loss \(2\,dB\), and design margin \(1\,dB\). The receiver input power is most nearly:

1. -6 dBm
2. -9 dBm
3. -12 dBm
4. -18 dBm

Solution

In dB link-budget arithmetic, subtract all losses and margins from launch power: \(-3-6-2-1=-12\,dBm\). Answer: -12 dBm. Reference lane: Electromagnetics and Fiber Optics > fiber links and loss budgets.

7. MOSFET Gate-Drive Power

A MOSFET gate has total gate charge \(Q_g = 45\,nC\), gate drive voltage \(V_g = 10\,V\), and switching frequency \(f_s = 100\,kHz\). The approximate gate-drive power is:

1. 4.5 mW
2. 45 mW
3. 0.45 W
4. 4.5 W

Solution

Use \(P_g=Q_gV_gf_s\). \(45\times10^{-9}\times10\times100\times10^3=0.045\,W=45\,mW\). Answer: 45 mW. Reference lane: Electronic Components > MOSFET switching and gate drive.

8. Common-Emitter Voltage Gain

A bypassed-emitter common-emitter stage has \(g_m=40\,mS\), \(R_C=3.3\,k\Omega\), and \(R_L=10\,k\Omega\). Using \(A_v\approx -g_m(R_C\parallel R_L)\), the gain is most nearly:

1. -9.9 V/V
2. -99 V/V
3. +99 V/V
4. -132 V/V

Solution

\(R_C\parallel R_L=(3.3k)(10k)/(13.3k)\approx2.48k\Omega\). Then \(A_v=-0.040(2480)\approx-99\,V/V\). Answer: -99 V/V. The negative sign comes from common-emitter inversion; using only \(R_C\) would overstate the gain magnitude.

9. First-Order Settling Time

A first-order control loop has time constant \(\tau=0.18\,s\). The approximate 2% settling time is most nearly:

1. 0.18 s
2. 0.36 s
3. 0.72 s
4. 1.8 s

Solution

For a first-order response, the 2% settling estimate is about \(4\tau\). \(4(0.18)=0.72\,s\). Answer: 0.72 s. Reference lane: Analog and Digital Control Systems > time response.

10. QPSK Symbol Rate

A telemetry link must deliver 12 Mb/s of information. A forward-error-correction code has rate \(3/4\), and QPSK carries 2 coded bits per symbol. The required symbol rate is most nearly:

1. 4 Msym/s
2. 6 Msym/s
3. 8 Msym/s
4. 16 Msym/s

Solution

The coded bit rate is \(12/(3/4)=16\,Mb/s\). QPSK carries 2 coded bits per symbol, so the symbol rate is \(16/2=8\,Msym/s\). Answer: 8 Msym/s. Reference lane: Communication Techniques > digital modulation and coding.

Answer Key

Problem	Answer	Topic lane
1	A	Electronics Circuits
2	C	Measurement and Instrumentation
3	D	Safety and Reliability
4	B	Signal Processing
5	B	Digital Systems
6	C	Electromagnetics and Fiber Optics
7	B	Electronic Components
8	B	Electronics Circuits
9	C	Analog and Digital Control Systems
10	C	Communication Techniques

Next Steps

These ten examples are a warm-up. The free app demo gives a fuller 20-question PE ECC set with multiple-choice, fill-in-blank, drag-and-drop, and hotspot items in the real study interface. The paid PE ECC bank adds full-length exam simulations, topic analytics, calculator drills, and the in-app reference panel.

FAQ

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