**High-Speed Optical Transceiver PCBs Design:**

**Microstrip or Stripline?**

In high-speed printed circuit boards design, Engineers usually face two choices: microstrip line and stripline. In most case,for high-speed PCB design under 10Gb/s,microstrip waveguide become the dominant waveguide structure largely because it could simplify designand cost lower.Some inherent advantages make the stripline becoming more and more important.It seems that PCB design engineers needn't worry too much about the difference between microstrip and stripline since previous design experience makes people believe that it is not a problem.In fact,when faced higher speed pcb design, we need to make a choice.So, microstrip or stripline?

**Structure of microstrip and stripline**

Figure1 microstrip and Stripline

Figure1 shows the different of structure between microstrip and stripline. A microstrip consists of a conductive strip (copper) and a wider ground plane(copper), separated by a dielectric layer (Er1).Between two wider ground plane(copper), separated by two dielectric layer (Er1 and Er2),there is a conductive strip (copper) in stripline. Internal conductor in stripline is commonly called the “hot conductor1” while the other two, always connected at signal ground, are called “cold” or “ground” conductors. If the dielectric layer Er2 is in stead of free space , stripline will become microstrip .

**Electromagnetic field distribution**

Figure2 Electric E and Magnetic H field lines for fundamental Quasi-TEM in Microstrip ^{1}and Stripline^{2,3}

High-speed signal in the conductor follows the basic principle of electromagnetic described by the maxwell's equations. In most cases,areas of signal transmission and transmission medium are passive, so the current density and charge density are zero. Electric field distribution is determined and constrained in free space and homogeneous medium. Determined electric field distribution decides the magnetic field distribution.EQ.1 is a simplified form of maxwell's equations in the passive free space, and it expresses the fact that electric and magnetic fields are perpendicular to the direction of propagation.

**a**_{y}(∂E_{x}/ ∂z=-μ.∂H_{y}/ ∂t)

**a**_{x}(ε. ∂E_{x}/ ∂t=-∂H_{y}/ ∂z) （EQ.1^{3}）

Electromagnetic described by EQ.1 is called TEM Wave. It has only two field components(E and H) aligned with the transverse coordinates: Ez =Hz = 0（EQ.2^{1}）.

Discontinuity of Normal component and continuous of tangential component of the electric field in different medium boundary led to the distortion. Asymmetric structure of msicrostrip must result in electric field distortion in the boundary of free space and the dielectric layer. Usually, Quasi-TEM mode is used to describe the transmission parameters of microstrip while stripline is true TEM Wave. Of course, using Quasi-TEM mode to describe stripline is a good approximation and the high accuracy completely meet the engineering requirements.

**Effective dielectric constant**** and Propagation Delay**

Figure3 Effective dielectric constant responses for identical 8 mil line width of microstrip circuits fabricated on a standard RO4350 laminate with normal copper conductor. Effective dielectric constant is different with the increase of thickness of 4350 and signal frequency which the frequency of green line is 40GHz and red one is 15GHz

In the description of figure2, it had clearly knew that part of the electric field energy of microstrip radiates into the air. If we take the infinity of the earth as another reference plane,it means that dielectric constant of the microstrip waveguide structure is between 1 and Er. In actuality, effective dielectric constant is commonly used in engineering design to describe the relationship.* *Hammerstad^{4} and Collins^{5} have shown that effective dielectric constant of microstrip is decided by four factors:the thickness and width of the waveguide structure, thickness of dielectric layer and high speed signal frequency. If T1＜＜H1 (figure 1), Hammerstad and Collins have presented an excellent approximate solution. However, this kind of approximation is not applicable in Engineering PCB design. Effective dielectric constant can be accurately calculated by Saturn PCB Design Tools. Figure3 offers a comparison of the same dielectric substrate, but with two different frequencies. In both cases, the PCB substrate is standard Rogers RO4350. Thinner dielectric produces greater dielectric constant and the difference caused by different frequency is smaller. Thinner dielectric increases the coupling coefficient and reduces the loss of electric field energy radiation

In most cases, Er1 is equal to Er2, which greatly simplify the form of effective dielectric constant of stripline.

Propagation delay (tPD) is the time required for a signal to travel from one point to another. Transmission line propagation delay is a function of the dielectric constant of the material. Relationship between effective dielectric and transmission delay are given by EQ3 and EQ4.

tPD _{microstrip} (ps/in)=85(0.475εff+0.67)^{1/2 }(EQ3^{6})

tPD _{stripline} (ps/in)=85(εff)^{1/ 2}(EQ4^{7})

Figure4 propagation delay of the microstrip (blue) and stripline (red)

Figure4 tells us that the propagation delay of the microstrip line is smaller than stripline under the same effective dielectric constant as effective dielectric constant is greater than 2.

**Propagation phase velocity**** and ****dispersion**

When derived the distribution of electromagnetic field, the time variable is usually ignored .Electromagnetic field spreads at high speed along the z axis in time domain,phase velocity Vp defines the propagation rate.

Vp=c/（ε_{ff}.μ_{r}）^{1/2} (EQ5^{8})

Where c is the propagation rate of light in free space(3*10^{8}m/s), εff is effective dielectric constant and μ_{r} is a multiplier related to the type of metal used as the conductor. For copper, the value of μ_{r} is assumed to be about unity (1).

Phase velocity Vp mainly depends on effective dielectric constant εff and εff of mcirostrip is associated with signal frequency.According to Fourier transform,when observed in the frequency domain, high-speed signal contains abundant odd frequency information. The different frequency components of high-speed signal in microstrip line correspond to different effective dielectric constant. So, according to the EQ5, phase velocity will also be different.

Figure5 Blue curve describes the relationship between the effective dielectric constant and frequency, while the red is the relationship between phase velocity and frequency

Setting microstrip line waveguide structure: line width of 10 mils, the dielectric layer thickness to 5 mils and PCB material for RO4350, we can calculate the phase velocity under the particular frequency. Higher speed signal frequency will slow phase velocity, phase velocity of 15 GHz is 0.2% slower than 5 GHz(Figure5). It is enough to cause a signal distortion, usually we call this kind of distortion as dispersion.

Asymmetric structure of microstrip line caused the dispersion, therefore it is called dispersion waveguide, while, is non-dispersion waveguide.

**Skin effect and ****Frequency-Dependent Conductor Losses**

Figure6 Skin effect of microstrip and stripline

Because of conductor loss, the distribution of electric current in the conductor is not homogeneous and related to the frequency. The dielectric materials used in PCBs are also not perfect insulators and there is a dc loss associated with the resistive drop across the dielectric material between the signal conductor and the reference plane. The current density propagation in conductor is calculated with the EQ.6^{8}

J=σ.E .e^{-z(}πfσμ^{)0.5}.cos(wt-z^{(}πfσμ^{)0.5}) EQ.6

When z=1/(πfσμ)^{0.5}, EQ.6 can be simplified as EQ.7.

J=J_{0}/e EQ.7.

Where J_{0} is current density in zero（z=0）. Current density in the conductor thickness direction is attenuating in the form of index.That is called skin effect. The skin depth δ is calculated with the EQ.8^{8}.

δ=1/(πfσμ)^{0.5} EQ.8

Figure6 shows the skin depth of microstrip line and stripline.The blue simulates the distribution of electric current in the conductor.

Signal loss caused by conductor is divided into two parts: dc loss and rc loss.Where dc loss depends primarily on the resistivity of the conductor and the total area（EQ9^{9}）.

R_{dc}=ρL/(Wt) EQ9

Where R_{dc} is the DC resistance (f=0)of the line, ρ the resistivity of the conductor material in ohmmeters,L the length of the line, W the conductor width, t the conductor thickness

Skin effect led to the rc loss. Rc loss of microstrip can be approximated by EQ10^{9},and rc loss of stripline can be approximated by EQ11^{9}.

R_{ac_microstrip}_{ }= (πfσμ)^{0.5} /W.(1/π+1/π^{2}.ln（4W/t)+W^{2}/( W^{2}+5.8HW+0.03H^{2}) ） EQ.10

R_{ac_stripline }=R_{ac_microstrip} (H1)// R_{ac_microstrip} (H2) EQ.11

The total loss,which is called Frequency-Dependent Conductor Losses,is vector sum of dc los and ac loss. If contrast EQ10 and EQ11, we can clearly know that conductor loss of stripline is smaller than conductor loss of microstrip .

**Knee frequency and radiation losses**

Figure7^{10} Comparison of actual test data from 1” GCPWG, 1” Top Ground Microstip and

1”StraightMicrostip Test Boards

In figure2, it had clearly knew that due to asymmetric structure part of the electric field energy of microstrip radiates into the air and this kind of loss is called radiation loss. No radiation loss exists in stripline.

In a certain frequency range, higher frequency of high-speed signal means smaller radiation loss. If frequency is greater than a certain value, radiation loss will increase sharply. That frequency is defined as knee frequency. The test results of Southwest Microwave, Inc.(Figure7)^{10} proved that the existence of knee frequency. Usually, the knee frequency of microstrip is less than 50 GHz and the knee frequency of stripline is infinity.

**Environmental Humidity**

PCB board typically works in high humidity environment. PCB materials such as FR4 have the property of water absorption^{2}, which means in a humid environment (100%), surface of microstrip will absorb moisture and DK value of the free space change. At the same time, the copper will be oxidized under the action of water molecules. Humidity environment will increase its dielectric loss of microstrip while it hardly affects the stripline.

As a conclusion, it may suggests that pcb engineers should better use stripline in high speed PCBs design since stripline waveguide structure has numerous benefits such as no radiation losse,non-dispersion,lower conductor losses and humidity environment resistance.It also can support true TEM wave propagation and has infinity knee frequency. Of course, compared with microstrip ,it needs higher cost and more complex designs.

*1,Microstrip, Stripline, and CPW Design **，**Iulian Rosu, YO3DAC / VA3IUL*

*2,Understanding PCBs for HigH-FreqUenCy Applications**，**John Coonrod*

*3,Advanced Signal Integrity for High-Speed Digital Designs, Stephen H.Hall, Howard L.Heck*

*4,Hammerstad,E.,and O.Jensen,1980,Accurate models for microstrip computer-aided design*

*5,Collins, Robert,1992,Foundations for Microwave Engineering *

*6, William R. Blood, Jr., MECL System Design Handbook(HB205/D, Rev. 1A May 1988), ONSemiconductor, August, 2000. *

*7.High-Speed Board Layout Guidelines,* *Altera Corporation ,May 2007*

*8, Engineering Electromagnetics,William H.Hayt,Jr,John A.Buck*

*Inc., 2007*

*9, High-Speed Digital System Design—A Handbook of Interconnect Theory and Design ,Practices Stephen, H. Hall ,Garrett W. Hall James A. McCall *

*10,* *Bill Rosas, “Optimizing Test Boards for 50 GHz End Launch Connectors: Grounded Coplanar Launches and Through Lines on 30mil Rogers RO4350B with Comparison to Microstrip,” Southwest Microwave *